a r X i v :h e p -t h /9711035v 1 5 N o v 1997CPTH-S566.119,HUTP-97/A049,MIT-CTP-2689
hep-th/9711035
November,1997
POSITIVITY CONSTRAINTS ON ANOMALIES IN SUPERSYMMETRIC GAUGE THEORIES D.Anselmi Centre de Physique Theorique,Ecole Polytechnique,F-91128Palaiseau Cedex,FRANCE J.Erlich and D.Z.Freedman Department of Mathematics and Center for Theoretical Physics,Massachusetts Institute of Technology,Cambridge MA 02139,USA A.A.Johansen Lyman Laboratory,Harvard University,Cambridge,MA 02138,USA Abstract The relation between the trace and R -current anomalies in supersymmetric theories implies that the U(1)R F 2,U(1)R and U(1)3R anomalies which are matched in studies of N =1Seiberg duality satisfy positivity constraints.Some constraints are rigorous and others conjectured as four-dimensional generalizations of the Zamolodchikov c -theorem.These constraints are tested in a large number of N =1supersymmetric gauge theories in the non-Abelian Coulomb
phase,and they are satis?ed in all renormalizable models with unique anomaly-free R -current,including those with accidental symmetry.Most striking is the fact that the ?ow of the Euler anomaly coe?cient,a UV ?a IR ,is always positive,as conjectured by Cardy.
1Introduction
The computation of chiral anomalies of the R-current and conserved?avor currents is one
of the important tools used to determine the non-perturbative infrared behavior of the many
supersymmetric gauge theories analyzed during the last few years.The anomaly coe?cients
are subject to rigorous positivity constraints by virtue of their relation to two-point functions
of currents and stress tensors,and to other constraints conjectured in connection with possible
four-dimensional analogues of the Zamolodchikov c-theorem[1].The two-point functions have
been considered[2]as central functions whose ultraviolet and infrared limits de?ne central
charges of super-conformal theories at the endpoints of the renormalization group?ow.The
positivity conditions are reasonably well known from studies of the trace anomaly for?eld
theories in external backgrounds.In supersymmetric theories the trace anomaly of the stress
tensor and conservation anomaly of the R-current are closely related,which leads[3]to positivity
constraints on chiral anomalies.
Two studies of positivity constraints in the SU(N c)series of SUSY gauge theories with N f
fundamental quark?avors have previously appeared.The?rst of these[4]analyzed the con?ned
and free magnetic phases for N c ?ow of central charges when there is an interacting IR?xed point were developed in[3]and applied to the conformal phase for3N c/2 the positive?ow,a UV?a IR>0,of the coe?cient a(g(μ))of the Euler term in the trace anomaly in an external gravitational background,where g(μ)is the gauge coupling at RG scaleμ.This result agrees with the conjecture of Cardy[5]that the Euler anomaly obeys a c-theorem.Positivity is also satis?ed in all non-supersymmetric theories tested[5,6].We shall refer to the inequality a UV?a IR>0as the a-theorem.The purpose of this paper is to present an extensive exploration of the rigorous positivity constraints and those associated with the a-theorem in many supersymmetric gauge theories with interacting IR?xed points (and some IR free models).We?nd that the a-theorem and other constraints are satis?ed in all renormalizable theories we have examined,and there are other results of interest. In Sec.2,which is largely a review of[3],the various anomalies,the theoretical basis of the positivity constraints and the computation of central charge?ows are discussed.In Sec. 3we discuss some general aspects of positivity constraints and the a-theorem in models with R-charges uniquely?xed by classical conservation and cancellation of internal anomalies.In some models an accidental symmetry has been postulated to preserve unitarity,and the central charges must be corrected accordingly.This is discussed in Sec. 4.In Sec.5,the positivity constraints are tested in many examples of renormalizable SUSY gauge models with uniquely determined R-charges.We also check the a-theorem for various types of?ows between conformal ?xed points.The situation of some non-renormalizable models is discussed in Sec.6.There are other models in which the conserved,anomaly free R-current is not unique.Our methods are less precise in this case,but we discuss an example in Sec.7.Sec.8contains a discussion of results and conclusions. 2Anomalies and Positivity Constraints The theoretical basis for the analysis of anomalies in supersymmetric theories comes from a combination of three fairly conventional ideas,namely A.The close relation between the trace anomaly of a four-dimensional ?eld theory with exter-nal sources for ?avor currents and stress tensor and the two point correlators J μ(x )J ν(y ) and T μν(x )T ρσ(y ) and their central charges. B.The close relation in a supersymmetric theory between the trace anomaly Θ=T μμ and the anomalous divergence of the R -current ?μR μ. C.The fact that anomalies of the R -current can be calculated at an infrared superconformal ?xed point using ’t Hooft anomaly matching.This is the standard procedure,and one way to explain it is to use the all orders anomaly free S -current of Kogan,Shifman,and Vainshtein [7].We now review these ideas brie?y.More details are contained in [2,3]. A.Trace anomaly and central charges We consider a supersymmetric gauge theory containing chiral super?elds Φαi in irreducible representations R i of the gauge group G .To simplify the discussion we assume that the super-potential W =0,but the treatment can be generalized to include non-vanishing superpotential,and this will be done in Sec.2C below. We consider a conserved current J μ(x )for a non-anomalous ?avor symmetry F of the theory,and we add a source B μ(x )for the current,e?ectively considering a new theory with an additional gauged U(1)symmetry but without kinetic terms for B μ.The source can be introduced as an external gauge super?eld B (x,θ,ˉθ)so supersymmetry is preserved.We also couple the theory to an external supergravity background,contained in a super?eld H a (x,θ,ˉθ ),but we discuss only the vierbein e a μ(x )and the component V μ(x )which is the source for the R μcurrent of the gauge theory. The trace anomaly of the theory then contains several terms Θ=1 32π2?b (g )B 2μν+?c (g )16π2(?R μνρσ)2+?c (g ) 16π2 3T (G )? i T (R i )(1?γi (g (μ))) .(2.2) Here T(G)and T(R i)are the Dynkin indices of the adjoint representation of G and the repre-sentation R i of the chiral super?eldΦαi,andγi/2is the anomalous dimension ofΦαi. The various external trace anomalies are contained in the three coe?cients?b(g),?c(g)and a(g).The free?eld(i.e.one-loop)values of?c and a have been known for many years[9].In a free theory of N0real scalars,N1/2Majorana spinors,and N1gauge vectors,the results are c= 1 720 (124N1+11N1/2+2N0).(2.3) In a supersymmetric gauge theory with N v=dim G gauge multiplets and Nχchiral multiplets these values regroup as c UV=1 48 (9N V+Nχ).(2.4) If T j i is the?avor matrix for the current Jμ(x)which is theˉθθcomponent of the super?eld 16π4 (2δμν??μ?ν)b(g(1/x)) 48π4Πμνρσ c(g(1/x)) x4 ,(2.8) whereΠμν=(?μ?ν?δμν2)andΠμνρσ=2ΠμνΠρσ?3(ΠμρΠνσ+ΠμσΠνρ)is the transverse traceless projector andΛis the dynamical scale of the theory.The central function c(g(1/x))is a positive RG invariant function.Its endpoint values c UV and c IR are also central charges.The second tensor structure in(2.8)arises because of the internal trace anomaly.It is proportional to β(g(1/x))and thus vanishes at critical points. The important point is that there is a close relation between the anomaly coe?cients?b(g(μ)) and?c(g(μ))and the central functions b(g(μ))and c(g(μ)).Namely?b(g(μ))and b(g(μ))di?er by terms proportional to β(g(μ)),so they coincide at RG?xed points.The same holds for?c(g(μ)) and c(g(μ)).This means that the end-point values of the anomaly coe?cients are rigorously positive.This is evident for the free?eld ultraviolet values in(2.3-2.5).The infrared values b IR and c IR must also be positive,and this is an important check on the hypothesis that the long distance dynamics of a theory is governed by an interacting?xed point. This important relation between trace anomaly coe?cients and current correlators was derived in[2,3]by an argument with the following ingredients: i.Since the explicit scale derivative of a renormalized correlator corresponds to the insertion of the integrated trace anomaly,the Jμ(x)Jν(0) correlator satis?es μ? 8π2 ?b(μ)(2δ μν??μ?ν)δ4(x)? ?β(g(μ)) ?μ b(g(1/x)) 8π2 ?b(g(μ))δ4(x)+β(g(μ)) x4 reg.(2.10) where?b(g(μ))is associated with the overall divergence at x=0. https://www.doczj.com/doc/f11543516.html,ing the method of di?erential renormalization[11]and the RG equation,one can resum a series in powers of(log xμ)k to derive a non-perturbative di?erential equation,namely β(g) ??b(g) c-theorems:In two dimensions Zamolodchikov established the c-theorem by constructing a function C(g(μ))as a linear combination of(suitably scaled) T zz T zz , T zzΘ and ΘΘ correlators which satis?es: ? μ C(g(μ))|g=g?=0(2.12) ?g C(g?)=c? where c?is the Virasoro central charge of the critical theory at the?xed point g=g?or, equivalently,the?xed point value of the external trace anomaly coe?cient 1 Θ= 2 [4]. (iv)SU(N c)N=1SUSY QCD in the non-Abelian Coulomb phase for3N c a UV?a IR)are positive in the models above.It is known that c UV?c IR is positive in the situations i)[6]and iii)[4]above,but negative in situation ii)[6]and changes sign from positive to negative as N f increases in the theories of iv).Thus a universal“c-theorem”is ruled out. In the Appendix below we present brief calculations to show that a b-theorem cannot hold in situations i)–iii)above,and it is known[3]not to hold in situation iv). Thus the a-theorem,a UV?a IR>0,emerges as the only surviving candidate for a universal theorem in four dimensions.The desired physical interpretation requires the existence of an A-function A(g(μ))which decreases monotonically from a UV to a IR and counts e?ective degrees of freedom at a given scale.Thus the relation a UV?a IR>0would make little physical sense unless a IR is positive.Indeed it has been argued[15]that a(g(μ))is positive at critical points if a conjectured quantum extension of the weak energy condition of general relativity is valid. Let us now summarize this discussion of the positivity properties of trace anomaly coe?-cients.The free-?eld values a UV,b UV,c UV are automatically positive.Positivity is rigorously required for b IR and c IR,and it is a useful test of our understanding of the infrared dynamics to check this property in models.We will also explore the conjectured a-theorem and the related condition a IR>0.We will also show that the“data”for N=1SUSY gauge theories in the non-Abelian Coulomb phase imply that there is no linear combination u(a UV?a IR)+v(c UV?c IR) which is positive in all models(except for v=0,u>0). B.Relation betweenΘand?μRμanomalies in SUSY/SG. In a supersymmetric theory in the external U(1)gauge and supergravity backgrounds discussed above,the divergence of the Rμcurrent and the trace of the stress tensor are components of a single super?eld.Therefore the supersymmetry partner of the trace anomalyΘof(2.1)is ?μ(√3g3 β(g)(F F)??b(g)24π2R R+5a(g)?3?c(g) 24π2 ?c W2?aΞ (2.15) where Jα˙α,W2andΞare the supercurrent,super-Weyl,and super-Euler super?elds respectively. This equation shows that all gravitational anomalies are described by the two functions?c(g) and a(g),and this is also the reason why the coe?cients of the third and?fth terms of(2.1) are related.An alternate derivation of(2.14)which does not require superspace technology was also given in[3]. The last three terms of(2.14)are essentially the same as the anomalies usually computed in studies of N=1Seiberg duality.It is this fact that leads to immediate positivity constraints on supersymmetry anomalies which we can test easily in the various models in the literature which?ow to infrared?xed points. https://www.doczj.com/doc/f11543516.html,puting infrared anomaly coe?cients. In this section we discuss how the infrared central charges b IR,c IR and a IR are related to the conventional U(1)R F2,U(1)R and U(1)3R anomalies.This is already quite clear,and some readers may wish to jump ahead to the?nal formulae at the end.However we do think that it is useful to derive this relation using the formalism of the all-orders anomaly-free Sμcurrent introduced in[7].The external anomalies of this current can be clearly seen to agree in the infrared limit with those of the Rμcurrent which is in the same multiplet as the stress tensor, and thus part of the N=1superconformal algebra of the infrared?xed point theory.A very clear explanation of the Sμcurrent is given in Section3of[7]for the case of general gauge group G and arbitrary superpotential W(φ).We summarize and exemplify the argument for the slightly simpler case of cubic W(φ). Gaugino?elds are denoted byλa(x),a=1,...,dim G,and scalar and fermionic components ofΦαi(x)byφαi(x)andψαi(x)respectively.The canonical Rμcurrent(which is the partner of the stress tensor),and the matter Konishi currents Kμi for each representation are Rμ=1 λaγμγ5λa?1ψiαγμγ5ψαi+2φiα?Dμφαi Kμi=1 ψiαγμγ5ψαi+ i ?Φαi +T(R i) 3 iγiΦαi?W48π2 3T(G)? i T(R i)(1?γi) F F(2.18) where|indicates theθ2component of the super?eld minus its adjoint.The anomaly-free R current usually stated in the literature for any given model is a speci?c linear combination (assumed unique here) Sμ0=Rμ+ 1 3 i(γ?i+γi)Φαi?W48π2 3T(G)? i T(R i)(1?(γ?i+γi)) F aμv Fμva,(2.20) cancel except those with coe?cientsγi.There is then a unique(?avor singlet)all-order con-served current Sμ=Rμ+ 1 Its divergence vanishes, ?μS μ=1?φαi +1 3 i (γ?i ?γi )K μi the contribution of the Konishi current decreases faster than the contribution of the S μcurrent which has no anomalous dimension.Thus the S μand R μoperators and their correlators agree in the long distance limit,as is required at the superconformal IR ?xed point.In the free UV limit γi →0,and S μ→S μ0.As we will see shortly this means that external anomalies of S μcoincide with those computed in the literature. We distinguish three classes of models in which one obtains unique S μ0and S μcurrents.The ?rst is the set of models with chiral ?elds in N f copies of a single (real)irreducible representation R (or N f ?elds in R ⊕3 1?3T (G )3 1?3T (G )R representations,respectively, and we use T (R )=T (3 1?2T (G )3γX K μX S μ=R μ+1N f T (R )?γ(g,f ) i (K μi + K μi )?1 R ⊕adj ,respectively.If there is an IR ?xed point,then both βf =3fγX /2and ?β (g )given in (2.2)must vanish,and it is easy to see that all coe?cients of the Konishi terms in(2.24)vanish if this occurs.The procedure may be extended to more general models with W=f Tr X k+1,k>2,using the modi?cation of(2.20)(see Section3of[7])for general superpotentials. Another common class of models resembles the“magnetic”version of SU(N c)SUSY QCD. There are N f?avors of quark and anti-quark?elds q and?q in conjugate representations R′and 3 1?3T(G′)3(2γq+γM)KμM,(2.25) and one can check again that the coe?cients of independent Konishi currents vanish exactly whenβg=βf=0. Because the operator Sμis exactly conserved without internal anomalies,’t Hooft anomaly matching[20]can be applied to calculate the anomalies of its matrix elements with other exactly conserved currents,such as?μ SμTρσTλτ .One argument for this(Sec3of[3])is the following. The operator equation?μSμ=0holds in the absence of sources,and it must remain local when sources are introduced.For an external metric source dimensional and symmetry considerations restrict the possible form of the matrix element to ?μSμ(x) =s0R?R(x)(2.26) where the right hand side is local.A priori s0(g(μ))could depend on the RG scaleμ.However, Sμin this case is an RG invariant operator,so matrix elements cannot depend on g(μ).There-fore s0must be a constant,hence1-loop exact.If we now use the fact that S and R coincide at long distances we have the chain of equalities ? RT T IR=? ST T IR=? ST T UV=? S0T T (2.27) where the last term simply includes the one loop graphs of the current S0and gives the U(1)R anomaly coe?cient quoted in the literature.Similar arguments justify the conventional calcu-lation of of U(1)R F F and U(1)3R anomalies. Formulae for anomaly coe?cients:The previous discussion enables us to write simple formulae for the infrared values of the anomaly coe?cients in terms of the anomaly-free R-charges quoted in the literature.For a chiral super?eldΦαi in the representation R i of dimension dim R i the R-charge r i is related toγ?i in the Sμ0current(2.19)by r i=(2+γ?i)/3. The quantities b IR,c IR and a IR are the infrared values of the trace anomaly coe?cients?b,?c and a in(2.1).They are normalized by the free?eld values in(2.4)and(2.5)and are related to R-current anomalies by(2.14).One then obtains b IR=?3U(1)R F2=3 ij(dim R i)(1?r i)T j i T i j c IR ?a IR =? 116(dim G + i (dim R i )(r i ?1))5a IR ?3c IR = 916(dim G + i (dim R i )(r i ?1)3)(2.28)c IR = 132(4dim G + i (dim R i )(1?r i )(5?9(1?r i )2)a IR =332(2dim G + i (dim R i )(1?r i )(1?3(1?r i )2)). Note that the R -charge of the fermionic component of Φαi is r i ?1and appears in these formulae,which are valid for theories in an interacting conformal phase with unique anomaly free R -charges and no accidental symmetry.The treatment is extended to include accidental symmetry and theories with nonunique R -charge in later sections. The hypothesis that there is a nontrivial infrared ?xed point in any given model is established by several consistency tests which in the past did not include the positivity conditions we have discussed.The set of infrared R -charges assigned in the literature is not guaranteed to produce positive b IR ,c IR ,a IR so the positivity constraints provide an additional check that the hypothesis of an interacting ?xed point is correct. The corresponding UV quantities are obtained from (2.28)by replacing r i →2/3,and one can check that (2.4)and (2.5)are reproduced when this is done.Thus for ?ows without gauge symmetry breaking the total ?ow of the central charges from the UV to the IR is due to the di?erence between the canonical and non-anomalous R -charges,and are given by the following formulae: b UV ?b IR =3 ij (dim R i )[(r i ?2 384 i (dim R i )(2?3r i )[(7?6r i )2?17](2.30) a UV ?a IR =1 ?g C (g )=0at a ?xed point.A monotonic interpolating A -function is not known in four dimensions but one can consider a candidate A-function obtained from a IR in(2.28)by replacing the infrared values of r i by their values calculated along the?ow, i.e.r i→(2+γi(g(μ)))/3.This candidate A-function naturally satis?es Zamolodchikov’s sta-tionarity condition at weak coupling.The analogous candidate C-function obtained from c IR of(2.28)does not. 3Models with Unique R-charge In this section we discuss the positivity conditions b IR>0,c IR>0,a IR>0and a UV?a IR>0 in a large set of models in the literature where the anomaly-free R-charge is unique.While some of these models will be considered in more detail in the next two sections,here we are going to analyze some general aspects.It is worth emphasizing that even though the positivity of b IR and c IR follows generally from unitarity constraints,the fact that they turn out to be positive in our approach is additional evidence that our understanding of the infrared dynamics is correct. The positivity constraint a UV?a IR>0deserves some comments.As explained above,the gravitational e?ective action depends on the functions a and c.It is natural to assume that a candidate C-function measuring the irreversibility of the RG?ow may be a universal model independent linear combination C=ua+vc.We are going to show that the only combination C=ua+vc which satis?es?C=u(a UV?a IR)+v(c UV?c IR)≥0for all models is just C=a.First note that since there are theories(e.g.SU(N c)SUSY QCD with N f<3N c)with c UV?c IR of either sign[3]and a UV?a IR positive,one must take u>0.It is then su?cient to assume u=1.Consider the electric version of Seiberg’s SU(N c)QCD with N f fundamental ?avors in the conformal window,3N c/2 Below we state simple su?cient conditions for the positivity constraints b IR>0,c IR>0, a IR>0,and also for a UV?a IR>0in the case of RG?ows from a free ultraviolet to an infrared ?xed point.Remarkably enough,these su?cient conditions can be quickly seen to be satis?ed in most of the conformal window of all renormalizable theories that we have analyzed.Closer examination is required for cases with accidental symmetry.There are also many examples of?ows between interacting?xed points which are generated by various deformations.These situations are discussed in later sections. A.Su?cient conditions We?rst note that in part of the conformal window of some models,the unitarity bound r≥2/3 fails for one or more composite operators of the chiral ring.Then the formulae(2.28)for infrared anomalies require correction for the ensuing accidental symmetry.Such cases are discussed separately in Sec.4,and we consider here models without accidental symmetry, which necessarily have r i≥1/3for all?elds of the microscopic theory. The simplest way in which the positivity conditions can be satis?ed is if the contributions to b IR,c IR and a IR in(2.28),and to a UV?a IR in(2.31),are separately positive for each contributing representation R i.This leads to the following su?cient conditions: (i)b IR>0if r i≤1for all chiral super?eldsΦi √5/3=1.745for allΦi (ii)c IR>0if1? √3=1.577for allΦi (iii)a IR>0if1?1/ (iv)a UV?a IR≥0if r i≤5/3for allΦi. In all of the models examined we?nd that in the part of the conformal window where no accidental symmetry is required, a.)remarkably,r i≤5/3for all renormalizable models,so the a-theorem is always satis?ed. √ b.)1? 3 Thus,most of the positivity conditions,especially the a-theorem,can be veri?ed essentially by inspection of the tables of R-charges presented in the literature on the various models. Actually,in many cases one can prove that r i<5/3as a consequence of asymptotic freedom in absence of accidental symmetry(i.e.when all r i≥1/3).Explicit check is then unnecessary. We illustrate this in three simple situations i)For models with N f copies of a single irreducible real representation R(or N f copies of R⊕ (orγ?=1?3T(G) N f T(R) R and r X=2/3. iii)We also consider models which have the same structure as magnetic SU(N c)SUSY QCD, namely N f?elds q in a real representation R′of a dual gauge group G′(or N f?elds q,?q in R′⊕ B.Flows between superconformal?xed points A conformal?xed point is characterized by the values of b,c and a.These values do not depend on the particular?ow which leads to or from this conformal theory.Therefore one may be interested in a computation of the?ow a UV?a IR for a theory which interpolates between two interacting conformal?xed points.Such an interpolation may be obtained by deforming a superconformal theory with a relevant operator which generates an RG?ow driving the theory to another superconformal?xed point.Since we know the conformal theories at both ultraviolet and infrared limits of this interpolating theory,the computation simply requires subtraction of the end-point central charges.In this case we do not need to construct any S-current interpolating between the ultraviolet and infrared conformal?xed points.However it is interesting that in some cases one can construct such an S-current and check directly the value of the?ow a UV?a IR.We discuss below aspects of various types of deformations.?Mass deformations. The simplest case is a mass deformation.Consider a conformal theory(H)characterized by a H,b H and c H which contains a chiral super?eldΦin a real representation of the gauge group(or a pair of chiral super?eldsΦand?Φin conjugate representations).Such a theory may be deformed by adding a gauge invariant mass term W m=m R representation and no superpotential.In this theory r=1?T(G)/2N f T(R) for the N f quarks of the theory H.We consider a mass deformation of H which leaves N f?n massless quarks in the theory L.These quarks have r=1?T(G)/2(N f?n)T(R).Substituting these charges in the formula(2.31)we subtract with the result a H?a L=9dim R T(G)3N2 f + 1 3 1?3T(G)3(1?γH)K Hμ, where the superscripts L and H indicate Konishi currents for the light and heavy quarks, respectively.Thusγ?H=1and r H=1so that the heavy quarks do not contribute to a IR=a L in(2.31).For the light quarksγ?L=1?3T(G)/2(N f?n)T(R)and r L=1?T(G)/2(N f?n)T(R) which is exactly the correct value in the low-energy theory of N f?n?avors.Thus the Sμcurrent analysis leads to the same value of a IR=a L used above. ?Higgs deformations. There are two qualitatively di?erent types of Higgs deformations.The?rst is a deformation along?at directions of the potential for the scalar?elds.Under such a deformation one generi-cally breaks both the gauge and?avor symmetries.While the Goldstone bosons corresponding to the gauge symmetry breaking are eaten by the Higgs mechanism,the Goldstone bosons of the?avor symmetry breaking remain in the massless spectrum of the theory.Therefore these Goldstone bosons(and their superpartners)have to be taken into account in the computation of the infrared values of a,b and c of the resulting theory.It is implicitly assumed in the literature that these Goldstone super?elds decouple from other light?elds of the low-energy theory and are free in the infrared.We thus assign r=2/3to these?elds. In general the positivity of the?ow a UV?a IR under the Higgs deformations is nontriv-ial evidence for the a-theorem.In a simple situation of?ow from the higgsed ultraviolet free theory to an infrared conformal?xed point the positivity of a UV?a IR follows from the fol-lowing argument.Let us consider an asymptotically free theory T.Let us also consider an asymptotically free theory T(1)which is a higgsed version of T along a?at direction and?ows to a nontrivial conformal theory in the infrared,CFT(1)IR.We are going to argue that the?ow a UV(T(1))?a(1)IR>0.We assume that there are n Goldstone chiral super?elds that decouple from the rest of the theory.It is convenient to de?ne another asymptotically free theory T(2) which is just the theory T(1)with all massive?elds dropped out plus n free chiral super?elds.Let us assume that the interacting part of the theory T(2)is also in its conformal window and?ows to a nontrivial conformal theory CFT(2)IR,and the a-theorem is satis?ed for this?ow.We have CFT(1)IR=CFT(2)IR⊕(n free chiral super?elds).Therefore instead of the?ow T(1)→CFT(1)IR one can consider the two step?ow T(1) UV→T(2)UV⊕(n free chiral super?elds)→CFT(1)IR(see Fig.1). Fig.1.The diagram of?ows under Higgs deformations. Since the a-theorem is trivially satis?ed for the?ow T(1) UV→T(2)UV⊕(n free chiral super?elds) we arrive at the conclusion that a UV(T(1))?a(1)IR>0. The second type of Higgs deformation is the magnetic counterpart of a mass term in the electric theory.To be concrete we consider SU(N c)SUSY QCD with electric quarks Q iαand anti-quarks Qαi,whereα=1...N c,and i=1,...,N f are color and?ower indices,respectively. The magnetic theory has G=SU(N f?N c)with quarks,anti-quarks and meson qαi,?q iα,and M i j.The mass perturbation W m=mQ N fα QαN f in the electric theory is mapped to W m=mM N f N f on the magnetic side[23]so that?avor symmetry is broken explicitly to SU(N f?1).Analysis ?q N f =0, [23]of the magnetic equations of motion shows that there is a Higgs e?ect with q N f so the gauge group is broken to SU(N f?N c?1).The spectrum contains massive?elds plus the light?elds of the magnetic e?ective low energy theory with G=SU(N f?N c?1)and N f?1?avors.If this theory is still in its conformal window,i.e.N f?1>3 MM.The?eld M is charged with respect to the current J(M) μbut the other?elds are not.In this case the perturbative anomaly free Sμcurrent can mix with the J(M) μcurrent under the RG?ow because the scaling dimension of the latter tends to the canonical dimension 3of a conserved current.Thus the infrared R current can be determined as an infrared limit of a linear combination R IRμ=Sμ+Aμ,(4.32) where Aμ=λJ(M) μ.The coe?cientλis?xed by the condition that R=2/3for the?eld M. Assuming that this picture is correct one can easily compute the infrared values of the central functions a,b and c.In the notation of Sec.2,one has to compute the three point correlators RRR IR and RT T IR.Substituting the expression(4.32)for Rμinto these correlators one has(the subscript IR is omitted here) RRR = SSS +3 SSA +3 SAA + AAA , RT T = ST T + AT T .(4.33) At this point we note that the correlators SSA , SAA , AAA and AT T are saturated by the free chiral?eld M and hence they can be easily computed,i.e.we have SSA = SSA free, SAA = SAA free, AAA = AAA free, AT T = AT T free. Thus the correlators RRR IR and RT T IR can be rewritten as follows: RRR IR= SSS + RRR free? SSS free, RT T IR= ST T + RT T free? ST T free.(4.34) As we explained in section2the central charges a IR and c IR are just given by linear combi-nations of the correlators RRR IR and RT T IR.We consider the case where there is one accidental U(1)symmetry for the gauge invariant composite super?eld M in an irreducible rep-resentation of the?avor group of dimension dim M(more general cases can easily be handled). The corrected infrared values of the central charges are dim M a IR=a(0)IR+ (2?3r M)[(7?6r M)2?17].(4.35) 384 Here we denoted by a(0)IR and c(0)IR the expressions for a and c given by equations(2.28),and r M stands for the S charge of the chiral?eld M,speci?cally the sum of the S charges of its elementary constituents.Since by assumption r<2/3it is easy to see that the correction to a √ is always positive.The correction to c is positive at r<(7? 17)/6 a IR and c IR positive,so the sign is important. In general the formulas for the infrared values of?avor central functions should also be corrected due to the presence of accidental symmetries.The general formula for the corrected b can be easily obtained along the above lines and reads b IR=b(0)IR+3T i j T j i r M?2 Here we denoted by b(0)IR the expression for b IR given in(2.28),T i j stands for the?avor generator associated with b.The correction dim M(r M?2/3)is always negative. Deformations of conformal?xed points with accidental symmetry.In the following we test various examples of superconformal models and?ows between them.In particular we will consider?ows from superconformal models with accidental symmetries taken as an ultraviolet ?xed point to di?erent infrared?xed points.Such a?ow may be generated by appropriate de-formation of the ultraviolet theory with a relevant operator.It is important that the ultraviolet theory has to be taken together with the free chiral?elds generating the accidental symmetry. In fact the deformation of the ultraviolet theory by a relevant operator generates a non-trivial coupling of the interacting part of the UV theory to the accidental chiral super?elds.This turns out to be important for positivity of a UV?a IR. 5Examples of models with uniquely de?ned S current and the ?ows In this section we give detailed results for the models that we have analyzed.We mainly focus on subtleties met in the computations of the infrared values of a and c. 5.1Models with one type of irreducible representation This class of models includes the SU(N c)series,SO(N c)series[23],Sp(2N c)series[24],Pouliot Spin(7)model[25],Distler-Karch models with exceptional groups[26].?Seiberg’s QCD with G=SU(N c),SO(N c)with N f,and Sp(2N c)with2N f fundamentals. Conformal windows are3N c/2 Table1.Flows from UV free theories to Seiberg’s conformal QCD. Gauge group a UV?a IR in magnetic theory N f N c N f 2 2+3N c12N f 2(3N2c+4N c N f+3N2f) N c(?6+2N f+3N c)(6+N f?3N c)2N c(?6?2N f+3N c)2(3N2f?6N c+4N c N f+3N2c) Sp(2N c) 24N2 f 24N2 f The models considered below have non-renormalizable magnetic versions.Therefore we discuss only the electric versions that are renormalizable.The results of our computations are given in Table2.Aspects of the RG?ows of non-renormalizable theories are considered in the next section. ?Spin(7)Pouliot model with N f spinors8,Q i.Conformal window:7≤N f≤14.We have in the infrared r IR8=1?5/N f.There is an accidental symmetry at N f=7due to decoupled QQ singlet.In Table2we separated the accidental corrections to a IR and c IR from the regular ones.Note that the correction to c IR turns out to be negative. ?G2with N f7.Conformal window:6≤N f≤11.We have R IR7=1?4/N f.The accidental symmetry point appears at N f=6where QQ has r=2/3and hence it is free.Therefore there are no accidental corrections to the central charges. ?E7Distler-Karch model:4fundamentals56,Q i;r Q=1/4. ?E6Distler-Karch model(I):6fundamentals27,Q i;r Q=1/3. ?E6Distler-Karch model(II):3×(27+ a IR electric theory, a free UV?a IR 123 4N2 f >0 8?1125N f N f 2 2+15 Spin(7)with N f=7spinors8 accidental symmetry 784+23 2352392?1311761176 21 N2 f >0 8?1267N f N f 2 1+6 E7with4fundamentals56 6464192 4510527 E6with matter in3×(27+4510527 F4with N f=5in26 20010075 1209 48=37391625 48 =48595413 Spin(8)with matter in 4×(8v+8c+8s) 888 5.2Deformations ?Deformations of SU(N c),SO(N c)and Sp(2N c)Seiberg QCD models.Higgsing of the Seiberg superconformal models corresponds to N c,N f→N′c=N c?1,N′f=N f?1.The infrared theory has2(N f?1)decoupled Goldstone gauge singlets for SU(N c)and Sp(2N c)models and N f?1for SO(N c). 1.Consider?rst the SU(N c)theory.In the region3N c/2 ultraviolet and infrared theories are in their conformal windows and we have ?a=1?N f 8? 9N4c 16(N f?1)2>0. In the cases N f=3N c?1,3N c?2the infrared theory is free since N′f=3N′c+1and N′f=3N′c respectively.The infrared value a IR is then computed using r=2/3for all chiral super?elds of the low-energy N′c,N′f theory and the Goldstone?elds.The results are ?a=?9+76N c?210N2c+180N3c16(?2+3N c)2 >0. 2.Consider the SO(N c)theory.In the region3(N c?2)/2 ?a=1?N f 32 2N f+8(N f?N c+2)?9 N c N f ?1 (N f?N c+2)2+ 3 N c(N f?1)2 (N f?N c+2)3 >0 In the cases of N f=3N c?7,3N c?8(in the latter case we limit ourselves to N c≥4for the ultraviolet theory to be in the conformal window)the infrared theory is free so that respectively ?a=?882+1756N c?1011N2c+180N3c16(?8+3N c)2 >0. 3.Consider the Sp(2N c)theory.In the region3(N c+1)/2 ?a=1?N f 32 6(3?4N f)+96(N f?N c?1)?108 N c+1N f ?1 (N f?N c?1)2+ 36 N c+1(N f?1)2 (N f?N c?1)3 >0. In the cases of N f=3N c+1,3N c+2the infrared theory is free so that respectively ?a=?3?16N c+41N2c+138N3c48(2+3N c)2 >0. The mass deformations obviously respect the a-theorem because?a/?N f>0in all cases(see explicit computation in Sec.3). ?Deformations of Spin(7)Pouliot model. First consider the higgsing of the Spin(7)Pouliot model with7≤N f≤14fundamentals to the G2model with N f?1fundamentals and N f?1Goldstone super?elds. in，on，at的时间用法和地点用法 一、in, on, at的时间用法 ①固定短语： in the morning/afternoon/evening在早晨/下午/傍晚, at noon/night在中午/夜晚, （不强调范围，强调的话用during the night） early in the morning=in the early morning在大清早， late at night在深夜 on the weekend在周末（英式用at the weekend在周末，at weekends每逢周末） on weekdays/weekends在工作日/周末， on school days/nights在上学日/上学的当天晚上， ②不加介词 this, that, last, next, every, one, yesterday, today, tomorrow, tonight，all，most等之前一般不加介词。如， this morning 今天早晨 （on）that day在那天（that day更常用些） last week上周 next year明年 the next month第二个月（以过去为起点的第二个月，next month以现在为起点的下个月） every day每天 one morning一天早晨 yesterday afternoon昨天下午 tomorrow morning明天早晨 all day/morning/night整天/整个早晨/整晚（等于the whole day/morning/night） most of the time （在）大多数时间 ③一般规则 除了前两点特殊用法之外，其他≤一天，用on，＞一天用in，在具体时刻或在某时用at（不强调时间范围） 关于on 生日、on my ninth birthday在我九岁生日那天 节日、on Teachers’Day在教师节 （注意：节日里有表人的词汇先复数再加s’所有格，如on Children’s Day, on Women’s Day, on Teachers Day有四个节日强调单数之意思，on Mother’s Day, on Father’s Day, on April Fool’s Day, on Valenti Day） 星期、on Sunday在周日，on Sunday morning在周日早晨 on the last Friday of each month 在每个月的最后一个星期五 日期、on June 2nd在六月二日 on the second (of June 2nd) 在六月的第二天即在六月二日 on the morning of June 2nd在六月二日的早晨，on a rainy morning在一个多雨的早晨 on a certain day 在某天 on the second day在第二天（以过去某天为参照） 注意：on Sunday在周日，on Sundays每逢周日（用复数表每逢之意），every Sunday每个周日，基本一个意思。 on a school day 在某个上学日，on school days每逢上学日。on the weekend在周末，on weekends每逢 周末。 关于in in June在六月 in June, 2010在2010年六月 常用标点符号用法简表 标点符号栏目对每一种汉语标点符号都有详细分析，下表中未完全添加链接，请需要的同学或朋友到该栏目查询。名称符号用法说明举例句号。表示一句话完了之后的停顿。中国共产党是全中国人民的领导核心。逗号，表示一句话中间的停顿。全世界各国人民的正义斗争，都是互相支持的。顿号、表示句中并列的词或词组之间的停顿。能源是发展农业、工业、国防、科学技术和提高人民生活的重要物质基础。分号；表示一句话中并列分句之间的停顿。不批判唯心论，就不能发展唯物论；不批判形而上学，就不能发展唯物辩证法。冒号：用以提示下文。马克思主义哲学告诉我们：正确的认识来源于社会实践。问号？用在问句之后。是谁创造了人类？是我们劳动群众。感情号①！1.表示强烈的感情。2.表示感叹句末尾的停顿。战无不胜的马克思主义、列宁主义、毛泽东思想万岁！引号 ②“ ” ‘ ’ ╗╚ ┐└1.表示引用的部分。毛泽东同志在《论十大关系》一文中说：“我们要调动一切直接的和间接的力量，为把我国建设成为一个强大的社会主义国家而奋斗。”2.表示特定的称谓或需要着重指出的部分。他们当中许多人是身体好、学习好、工作好的“三好”学生。 3.表示讽刺或否定的意思。这伙政治骗子恬不知耻地自封为“理论家”。括号③（）表示文中注释的部分。这篇小说环境描写十分出色，它的描写（无论是野外，或是室内）处处与故事的发展扣得很紧。省略号④……表示文中省略的部分。这个县办工厂现在可以生产车床、电机、变压器、水泵、电线……上百种产品。破折号⑤——1.表示底下是解释、说明的部 分，有括号的作用。知识的问题是一个科学问题，来不得半点的虚伪和骄 傲，决定地需要的倒是其反面——诚实和谦逊的态度。2.表示意思的递进。 团结——批评和自我批评——团结3.表示意思的转折。很白很亮的一堆洋 钱！而且是他的——现在不见了！连接号⑥—1.表示时间、地点、数目等 的起止。抗日战争时期（1937-1945年）“北京—上海”直达快车2.表 示相关的人或事物的联系。亚洲—太平洋地区书名号⑦《》〈〉表示 书籍、文件、报刊、文章等的名称。《矛盾论》《中华人民共和国宪法》《人 民日报》《红旗》杂志《学习〈为人民服务〉》间隔号·1.表示月份和日期 之间的分界。一二·九运动2.表示某些民族人名中的音界。诺尔曼·白求 恩着重号.表示文中需要强调的部分。学习马克思列宁主义，要按照毛泽 东同志倡导的方法，理论联系实际。······ In\ on\ at (time) at 用在具体某一时刻eg at 11:00 at 4:30 在节假日的全部日子里at Christmas 习惯用法at noon at weekends\ at the weekend at night at breakfast\lunch\supper on 具体到某一天；某一天的早晨，中午或晚上on May the first on Sunday morning 对具体某一天的早晨，中午，晚上进行详细的描述on a sunny morning on a windy night 节日的当天；星期on Women?s Day on Monday In 用在年；月；季节in spring in 2012 in August 后面+一段时间表示将来时in two days 习惯用法in the morning\in the afternoon\in the evening “\”以this, that, last, next, some, every, one, any,all开始的时间副词之前的at\on\in 省略在today, tomorrow, yesterday, the day after tomorrow, tomorrow morning，yesterday afternoon，the day before yesterday 之前的介词必须省略 Practice ___ summer ____ 2012 ____ supper ___ 4:00 ___ June the first ___yesterday morning ____ New Year?s Day ___ Women?s Day ___ the morning ____ the morning of July the first ____ 2014 ___ tomorrow morning ____ midnight 1.—What are you doing ____ Sunday? And what is your wife doing ___ the weekend? 2. He?ll see you ____ Monday. And he…ll see your brother ____next Monday. 3. They often go out ___ the evenings. But they don?t go out ____ Sunday evenings. 4. Do you work ____ Fridays? Does she work _____ every Friday? 5. They usually have a long holiday ___ summer. But their son can only have a short holiday ___ Christmas. 6. Paul got married ___ 2010, He got married ___ 9 o?clock ___ 19 May 2010. His brother got married ___ May, 2011. His sister is getting married ___ this year. 1.—When will Mr Black come to Beijing? ---_______ September 5 A. on B. to C. at D. in 2. The twins were born ____ a Friday evening. A. on B. of C. at D. in 3. It?s the best time to plant ____ spring. A. on B. in C. at D.\ 4. ____ the age of twelve, Edison began selling newspaper on train. A. On B. At C. In D.By 5. She has been an English teacher ____ 2000. A. for B. since C. in D.on 6.I have studied English _____ 2003. A. since B. for C. from D.in 一、基本定义 句子，前后都有停顿，并带有一定的句调，表示相对完整的意义。句子前后或中间的停顿，在口头语言中，表现出来就是时间间隔，在书面语言中，就用标点符号来表示。一般来说，汉语中的句子分以下几种： 陈述句： 用来说明事实的句子。 祈使句： 用来要求听话人做某件事情的句子。 疑问句： 用来提出问题的句子。 感叹句： 用来抒发某种强烈感情的句子。 复句、分句： 意思上有密切联系的小句子组织在一起构成一个大句子。这样的大句子叫复句，复句中的每个小句子叫分句。 构成句子的语言单位是词语，即词和短语（词组）。词即最小的能独立运用的语言单位。短语，即由两个或两个以上的词按一定的语法规则组成的表达一定意义的语言单位，也叫词组。 标点符号是书面语言的有机组成部分，是书面语言不可缺少的辅助工具。它帮助人们确切地表达思想感情和理解书面语言。 二、用法简表 名称 句号① 问号符号用法说明。？1．用于陈述句的末尾。 2．用于语气舒缓的祈使句末尾。 1．用于疑问句的末尾。 2．用于反问句的末尾。 1．用于感叹句的末尾。 叹号！ 2．用于语气强烈的祈使句末尾。 3．用于语气强烈的反问句末尾。举例 xx是xx的首都。 请您稍等一下。 他叫什么名字？ 难道你不了解我吗？为祖国的繁荣昌盛而奋斗！停止射击！ 我哪里比得上他呀！ 1．句子内部主语与谓语之间如需停顿，用逗号。我们看得见的星星，绝大多数是恒星。 2．句子内部动词与宾语之间如需停顿，用逗号。应该看到，科学需要一个人贡献出毕生的精力。 3．句子内部状语后边如需停顿，用逗号。对于这个城市，他并不陌生。 4．复句内各分句之间的停顿，除了有时要用分号据说苏州园林有一百多处，我到过的不外，都要用逗号。过十多处。 顿号、用于句子内部并列词语之间的停顿。 介词in on at 表示时间的用法及区别 Step1 Teaching Aims 教学生掌握时间介词in,on和at的区别及用法。 Step2 Teaching Key and Difficult Points 教学生掌握时间介词in,on和at的区别及用法。 Step3 Teaching Procedures 1.用in的场合后所接的都是较长时间 (1)表示“在某世纪/某年代/特定世纪某年代/年/季节/月”这个含义时，须用介词in Eg: This machine was invented in the eighteenth century. 这台机器是在18世纪发明的。 、 She came to this city in 1980. 他于1980年来到这个城市。 It often rains here in summer. 夏天这里常常下雨。 (2)表示“从现在起一段时间以后”时，须用介词in。(in+段时间表将来) Eg: They will go to see you in a week. 他们将在一周后去看望你。 I will be back in a month. 我将在一个月后回来。 (3)泛指一般意义的上、下午、晚上用in, in the morning / evening / afternoon Eg: They sometimes play games in the afternoon. 他们有时在下午做游戏。 Don't watch TV too much in the evening. 晚上看电视不要太多。（4）A. 当morning, evening, afternoon被of短语修饰，习惯上应用on, 而不用in. Eg: on the afternoon of August 1st & B. 但若前面的修饰词是early, late时，虽有of短语修饰，习惯上应用in, 而不用on. Eg: in the early morning of September 10th 在9月10的清晨； Early in the morning of National Day, I got up to catch the first bus to the zoo. 国庆节一清早，我便起床去赶到动物园的第一班公共汽车。 2.用on的场合后所接的时间多与日期有关 （1）表示“在具体的某一天”或（在具体的某一天的）早上、中午、晚上”，或“在某一天或某一天的上午，下午，晚上”等，须用介 介词in, on, at在表示时间时的用法区别 ①in时间范围大（一天以上）如：in Tanuary, in winter, in 1999;泛指在上午，下午，晚上，如：in the morning(afternoon, evening). 习惯用法：in the daytime 在白天。 ②on指在某一天或某一天的上午，下午，晚上，如：on Monday, on Sunday afternoon, on July 1, 1999 ③at时间最短，一般表示点时间，如at six o’clock, at three thirty.习惯用法：at night, at noon, at this time of year. in, on和at在表达时间方面的区别 in 表示在某年、某季节、某月、某周、某天和某段时间 in a year在一年中 in spring 在春季 in September 在九月 in a week 在一周中 in the morning/afternoon/evening 在上午/下午/傍晚 但在中午，在夜晚则用at noon/night on 表示某一天或某一天的某段时间 on Monday 在周一 on Monday afternoon 在周一下午 on March 7th 在3月7日 on March 7th, 1998. 在1998年3月7日 on the morning of March 7th, 1998. 在1998年3月7日上午 at 表示某个具体时刻。 at eight o’clock 在8点钟 at this time of the year 在一年中的这个时候 at the moment 在那一时刻 at that time 在那时 注意：在英语中，如果时间名词前用this, last, next 等修饰时，像这样的表示，“在某时”的时间短语前，并不需要任何介词。 例如：last month, last week, this year, this week, next year, the next day, the next year 等。 1．What’s the weather like in spring/summer/autumn/winter in your country? 你们国家春天/夏天/秋天/冬天的天气怎么样？ in 在年、月、周较长时间内 in a week 在里面 in the room 用某种语言 in English 穿着 in red on 某日、某日的上下午on Sunday afternoon 在……上面 on the desk 靠吃……为生live on rice 关于 a book on Physics 〔误〕We got to the top of the mountain in daybreak. 〔正〕We got to the top of the mountain at day break. 〔析〕at用于具体时刻之前，如：sunrise, midday, noon, sunset, midnight, night。〔误〕Don't sleep at daytime 〔正〕Don't sleep in daytime. 〔析〕in 要用于较长的一段时间之内，如：in the morning / afternoon, 或in the week / month / year. 或in spring / supper /autumn / winter等等。 〔误〕We visited the old man in Sunday afternoon. 〔正〕We visited the old man on Sunday afternoon. 〔析〕in the morning, in the afternoon 如果在这两个短语中加入任何修饰词其前面的介 精心整理in，on，at的时间用法和地点用法 一、in,on,at的时间用法 1、固定短语： inthemorning/afternoon/evening在早晨/下午/傍晚, 2 （on thenextmonth第二个月（以过去为起点的第二个月，nextmonth以现在为起点的下个月） everyday每天 onemorning一天早晨 yesterdayafternoon昨天下午 tomorrowmorning明天早晨 allday/morning/night整天/整个早晨/整晚（等于thewholeday/morning/night）mostofthetime（在）大多数时间 3、一般规则 除了前两点特殊用法之外，其他≤一天，用on，＞一天用in，在具体时刻或在某时用at（不强调时间范围） 关于 On 1 2) 3) （注意：节日里有表人的词汇先复数再加s’所有格，如 onChildren’sDay,onWomen’sDay,onTeachers’Day有四个节日强调单数之意思，onMother’sDay,onFather’sDay,onAprilFool’sDay,onValentine’sDay） 星期、onSunday在周日，onSundaymorning在周日早晨onthelastFridayofeachmonth在每个月的最后一个星期五 日期、onJune2nd在六月二日 onthesecond(ofJune2nd)在六月的第二天即在六月二日onthemorningofJune2nd在六月二日的早晨，onarainymorning在一个多雨的早晨 onacertainday在某天 onthesecondday在第二天（以过去某天为参照） 关于 In 1 2) InJune在六月 inJune,2010在2010年六月 in2010在2010年 inamonth/year在一个月/年里（在将来时里翻译成一个月/年之后） inspring在春天 常用标点符号主要用法 问号 1、用在特指问句后。如：(7)你今年多大了？ 2、用在反问句后。如：(8)为什么我们不能刻苦一点呢？ ?提示：反问句若语气缓和，末尾可用句号；若语气重可用感叹号。如：(9)国家 主席可以活活被整死；堂堂大元帅受辱骂；……这哪里还有什么尊重可言！ 3、用在设问句后。如：(10)我们能让你计划实现吗？不会的。 4、用在选择问句中。如：(11)我们是革命呢，还是要现大洋？ ( 12)你到底是去，还是不去？ 5、用在表疑问的独词句后。如：(13)我？不可能吧。 ?提示：若疑问句为倒装句，问号应放在句末。如：(14)到底出了什么问题，你的 车？(若说成：“到底出了什么问题？你的车。”则错误。) ?特别提示： 句号、问号均表示句末停顿。句号用于陈述句末尾，问号用于疑问句末尾。有些句 中虽有疑问词，但全句并不是疑问句，句末只能用句号，不能用问号。 例如：(17)……最后应求出铜块的体积是多少？ (18)面对千姿百态、纷繁芜杂的期刊世界，有哪位期刊编辑不想通过期刊版面设 计为刊物分朱布白、添花增色呢？ (19)关于什么是智力？国内外争论多年也没有定论。 (17) (18) ( 19)三句都是非疑问句，(17) (18)句中问号均应改为句号，(19)句中的问号应改为逗号。 感叹号 ?特别提示： 1、在表感叹或祈使语气的主谓倒装句中，感叹号要放在句末。 如：(20)多么雄伟壮观啊，万里长城！ 2、句前有叹词，后是感叹句，叹号放在句末。 如：(21)啊，这儿多么美丽！ 下面介绍句中点号的用法。句中点号包括逗号、分号、顿号、和冒号四种。 逗号 提示：复句内各分句之间的停顿，除了有时用分号外，都要用逗号。 顿号 用于句中并列的词、词组之间较小的停顿。 如：(22)邓颖超的品德、人格、风范为中华民族树立了一座精神丰碑。 (23)从1918年起，鲁迅陆续发表了《狂人日记》、《药》、《祝福》等短篇小说。 ?特别提示：以下九种情况不用顿号。 1、不定数的两个数字间不用顿号。 如：(24)你的年龄大概是十六七岁。(不能写成“十六、七岁”) ?【注意】相邻的两个数字而非约数之间要用顿号。 i n o n a t的时间用法和 地点用法版 集团档案编码：[YTTR-YTPT28-YTNTL98-UYTYNN08] i n，o n，a t的时间用法和地点用法 一、in,on,at的时间用法 1、固定短语： inthemorning/afternoon/evening在早晨/下午/傍晚, atnoon/night在中午/夜晚,（不强调范围，强调的话用duringthenight）earlyinthemorning=intheearlymorning在大清早， lateatnight在深夜 ontheweekend在周末（英式用attheweekend在周末，atweekends每逢周末）onweekdays/weekends在工作日/周末， onschooldays/nights在上学日/上学的当天晚上， 2、不加介词 this,that,last,next,every,one,yesterday,today,tomorrow,tonight，all，most等之前一般不加介词。如， thismorning今天早晨 （on）thatday在那天（thatday更常用些） lastweek上周 nextyear明年 thenextmonth第二个月（以过去为起点的第二个月，nextmonth以现在为起点的下个月） everyday每天 onemorning一天早晨 yesterdayafternoon昨天下午 tomorrowmorning明天早晨 allday/morning/night整天/整个早晨/整晚（等于 thewholeday/morning/night） mostofthetime（在）大多数时间 3、一般规则 除了前两点特殊用法之外，其他≤一天，用on，＞一天用in，在具体时刻或在某时用at（不强调时间范围） 关于on On指时间表示： 1）具体的时日和一个特定的时间，如某日，某节日，星期几等。Hewillcometomeetusonourarrival. OnMay4th(OnSunday,OnNewYear’sday,OnChristmasDay),therewillbeacelebra tion. 2)在某个特定的早晨，下午或晚上。 Hearrivedat10o’clocko nthenightofthe5th. Hediedontheeveofvictory. 3)准时，按时。 Iftherainshouldbeontime,Ishouldreachhomebeforedark. 生日、onmyninthbirthday在我九岁生日那天 节日、onTeachers’Day在教师节 （注意：节日里有表人的词汇先复数再加s’所有格，如 onChildren’sDay,onWomen’sDay,onTeachers’Day有四个节日强调单数之意思， onMother’sDay,onFather’sDay,onAprilFool’sDay,onValentine’sDay）星期、onSunday在周日，onSundaymorning在周日早晨 介词in,on与at表时间的用法 at < 天(eg. noon, dawn, night, one’ clock) on = 天(Monday, 30th June, New Year’s Day, Mother’s Day) in > 天(2008, summer, April, 还有早午晚) 用in的场合后所接的都是较长时间 (1)表示“在某世纪/某年代/特定世纪某年代/年/季节/月”这个含义时,须用介词in Eg: This machine was invented in the eighteenth century. 这台机器是在18世纪发明的。 This incident happened in the 1970s. 该事件发生在20世纪70年代。 She came to this city in 1980. 他于1980年来到这个城市。 It often rains here in summer. 夏天这里常常下雨。 (2)表示“从现在起一段时间以后”时,须用介词in。(in+段时间表将来) Eg: They will go to see you in a week. 他们将在一周后去看望你。 I will be back in a month. 我将在一个月后回来。 (3)泛指一般意义的上、下午、晚上用in, in the morning / evening / afternoon Eg: They sometimes play games in the afternoon. 他们有时在下午做游戏。 Don't watch TV too much in the evening. 晚上看电视不要太多。 (4)A. 当morning, evening, afternoon被of短语修饰,习惯上应用on, 而不用in. Eg: on the afternoon of August 1st (5)B. 但若前面的修饰词是early, late时,虽有of短语修饰,习惯上应用in, 而不用on. Eg: in the early morning of September 10th 在9月10的清晨; in the late afternoon of September 12th 在9月12日的傍晚。 Early in the morning of National Day, I got up to catch the first bus to the zoo. 国庆节一清早,我便起床去赶到动物园的第一班公共汽车。 用on的场合后所接的时间多与日期有关 (1)表示“在具体的某一天”或(在具体的某一天的)早上、中午、晚上”,或“在某一天或 某一天的上午,下午,晚上”等,须用介词on。 Eg: Jack was born on May 10th, 1982. 杰克生于1982年5月10日。 They left on a rainy morning. 他们是在一个雨天的早上离开的。 He went back to America on a summer afternoon. 他于一个夏天的下午返回了美国。 公文写作中标点符号的使用规范 《中华人民共和国国家标准》（GB|T15834—1995）中有《标点符号用法》，其中对标点符号的使用作了明确的规定： 标点符号是辅助文字记录语言的符号，是书面语的有机组成部分，用来表示停顿、语气以及词语的性质和作用。 常用的标点符号有16种，分点号和标号两大类。 点号的作用在于点断，主要表示说话时的停顿和语气。点号又分为句末点号和句内点号——句末点号用在句末，有句号、问号、叹号3种，表示句末的停顿，同时表示句子的语气；句内点号用在句内，有逗号、顿号、分号、冒号4种，表示句内的各种不同性质的停顿。 标号的作用在于标明，主要标明语句的性质和作用。常用的标号有9种，即：引号、括号、破折号、省略号、着重号、连接号、间隔号、书名号和专名号。 一、常用标点符号用法简表 名称符号用法说明举例 句号。表示一句话完了之后的停 顿。 中国共产党是全中国人民的领导核心。 逗号，表示一句话中间的停顿。全世界各国人民的正义斗争，都是互相支持的。 顿号、表示句中并列的词或词组 之间的停顿。 能源是发展农业、工业、国防、科学技术和提高人 民生活的重要物质基础。 分号；表示一句话中并列分句之 间的停顿。 不批判唯心论，就不能发展唯物论；不批判形而上 学，就不能发展唯物辩证法。 冒号：用以提示下文。马克思主义哲学告诉我们：正确的认识来源于社会实践。 问号？用在问句之后。是谁创造了人类？是我们劳动群众。 感情号！1.表示强烈的感情。 2.表示感叹句末尾的停 顿。 战无不胜的马克思主义、列宁主义、毛泽东思想万 岁！ 引号“”1.表示引用的部分。毛泽东同志在《论十大关系》一文中说：“我们要 七年级语文常用标点符号用法简表 七年级常用标点符号用法简表 一、基本定义 句子，前后都有停顿，并带有一定的句调，表示相对完整的意义。句子前后或中间的停顿，在口头语言中，表现出来就是时间间隔，在书面语言中，就用标点符号来表示。 二、复习标点符号的写法，明确标点符号的书写位置。 常用的标点符号有16种，分为点号和标号。 点号 句号 。 问号 ？ 感叹号 ！ 逗号 顿号 分号 ； 冒号 标号 引号“”‘’括号[] 破折号——省略号……书名号 着重号· 间隔号· 连接号— 专名号____ 备注占两格左上角 右上角 各占 一格 各占 一格 占两格 每格 三个点 占两格 标字下 标字间 占一格 标字下点号表示语言中的停顿，一般用在句中或句末。标号主要标明语句的性质和作用。 标点符号的书写位置。 在横行书写的文稿中，句号、问号、叹号、逗号、顿号、分号和冒号都占一个字的位置，放在句末的左下角。这七种符号通常不能放在一行的开头，因为这些符号表示语气的停顿，应该紧跟在一句话的末尾。如果一行的最后的一个格正好被文字占用了，那么这个标点就必须点标在紧靠文字的右下角。 引号、括号、书名号的前一半和后一半都各占一个字的 位置，它们的前一半可以放在一行的开头，但不出现在一行的末尾，后一半不出现在一行的开头。 破折号和省略号都占两个字的位置，可以放在一行的开头，也可以放在一行的末尾，但不可以把一个符号分成两段。这两种符号的位置都写在行次中间。） 引用之语未独立，标点符号引号外；引用之语能独立，标点符号引号里。 注意事项： 冒号 表示提示性话语之后的停顿，用来提引下文。 ①同志们，朋友们：现在开会了。 ②他十分惊讶地说：“啊，原来是你！” ③北京紫禁城有四座城门：午门、神武门、东华门和西华门。 注意：“某某说”在引语前，用冒号；在引语中或引语后，则不用冒号。如： ⑴老师说：“李白是唐代的大诗人，中学课本有不少李白的诗。” ⑵“李白是唐代的大诗人，”老师说，“中学课本里有不少李白的诗。” ⑶“李白是唐代的大诗人，中学课本里有不少李白的诗。”老师说。 时间介词(at, in ,on) 的用法 1. at （1）时间的一点、时刻等。如： They came home at seven o’clock. (at night, at noon, at midnight, at ten o’clock, at daybreak, at dawn）. （2）后面接表示岁数的词。 Children in China start school at 6 years old. （3）较短暂的一段时间。可指某个节日或被认为是一年中标志大事的日子。如： He went home at Christmas （at New Year, at the Spring Festival）. 2. in （1）在某个较长的时间（如世纪、朝代、年、月、季节以及泛指的上午、下午或傍晚等） 内。如： in 2004, in March, in spring, in the morning, in the evening, etc （2）在一段时间之后,常用于将来时。 He will arrive in two hours. These products will be produced in a month. 3. on （1）具体的时日和一个特定的时间，如某日、某节日、星期几等。如： On Christmas Day（On May 4th）, there will be a celebration. （2）在某个特定的早晨、下午或晚上。如： He arrived at 10 o’clock on the night of the 5th. （3）准时，按时。如： If the train should be on time, I should reach home before dark. 表示频率的副词用法详解 一、常见的频率副词 always，usually，often，sometimes， seldom，never. 1) always表示的频率为100%，意思是"总是、一直、始终"。 I always do my cleaning on Sundays. 我总是在星期天搞卫生。 2）usually与always相比，表示的频率要低些，约为70%-80%。意思是"通常"。 Plants are usually green. 植物通常是绿色的。 Usually she goes to work by bus. 她通常乘公共汽车去上班。 3）often的频率比usually又略低些，约为60%-70%，意思是"经常"、"常常"。 Do you often write to them? 你常给他们写信吗？ Does Fred come here often? 弗雷德常来这儿吗？ 4）sometimes的频率比often又低些，约为50%＞sometimes＞30%，意思是“有时、不时”。(window.cproArray = window.cproArray || []).push({ id: "u3054369" }); 3 公文中标点符号的正确用法 标点符号是公文语言的重要组成部分，可以帮助我们分清句子结构，辩明不同的语气，确切理解词语的性质和文章的意义，是公文语言的重要辅助工具。 一、标题中标点符号的用法 公文的标题，即一级标题的末尾，一般不加标点符号。例如：关于我县对《省市共建大西安意见》的几点建议，后面就不用标点符号。公文标题的内部，除用书名号和引号外，尽量不用标点符号。例如：关于对《咸阳市被征地农民就业培训和社会养老保险试行办法（征求意见稿）》的几点建议。正如有些书名号在标题中必须使用一样，有时引号也是不得不用的。例1：关于召开全县迎“双节”暨旅游工作会议的通知。例2：在全县“四防”工作会议上的讲话。例3：在推进迎接党的十八大消防安保工作暨“人人参与消防?共创平安和谐”启动仪式上的讲话。例4：关于实施“森林围城”计划的报告。“双节”、“四防”都有特定的内涵，是工作称谓的高度概括，属于特指，必须加注引号，以起到强调、提示的作用；“人人参与消防?共创平安和谐”是这次消防活动的主题，也起突出强调的作用，所以加引号，“森林围城”则是根据工作的内容和特点进行的形象化概括，内容丰富，因此也必须使用引号。与此类似的情况也并不少见，比如“863”计划、“三?八”妇女节、“9?8”投洽会、“一控双达标”、“双增双提”、“两个确保”等等。使用引号的原因一般是为了对一个特殊的概念或缩略语进行标注，以使读者明白这个词语具有特殊意义。但是，在公文标题中使用引号也要慎重，因为引号在标题中要比其它标点符号更显眼，如果可能，还是以尽量少用或不用为宜。例如：标题“构筑绿色屏障建设美丽彬县”。 公文内容里面的标题，即二、三级标题的末尾，如果是居中标题，一般也不加标点符号。例如下面三个二级标题：“过去五年工作回顾”、“今后五年奋斗目 关于常用序号的几点说明 一、结构层次序数 第一层为“一、二、三、”，第二层为“（一）（二）（三）”，第三层为“1.2.3.”第四层为“（1）（2）（3）”第五层为“①②③”。 二、文字材料中序号标点的正确使用 （一）“第一”、“第二”、“首先”、“其次”等后面应用逗号“，”。 （二）“一”、“二”、“三”等后面应用顿号“、”。 （三）“1”、“2”、“3”和“A”、“B”、“C”等后面应用齐线墨点（“.”），而不用顿号（“、”）或其它。 （四）序号如加括号，如（一）（二）（三），（1）（2）（3）等后面不加标点符号。 三、年份的正确书写 年份如用“二○○八年四月五日”的方式表述，则中间的“○”不能写成阿拉伯数字“O”或英语全角字符“o”。 四、汉语拼音的正确使用 （一）大小写：句子的首字母大写；诗行的首字母大写；专有名词每个词首字母大字；标题可以全部大写。 （二）分连写：词内连写，词间分写。 五、正确区分连接号和破折号 （一）凡文中使用连接号的应使用“～”，而不使用“——”或者“―”。 如：2008年3月～4月中的“～”，而不使用“——”或者“―”。 （二）凡文中使用破折号的应使用占两个空格的“——”而不用“～”或只占一个空格的“―”。如：再接再厉，推进语言文字规范化工作——2004年语言文字工作总结。 常用标点符号用法简表 一、基本定义 句子，前后都有停顿，并带有一定的句调，表示相对完整的意义。句子前后或中间的停顿，在口头语言中，表现出来就是时间间隔，在书面语言中，就用标点符号来表示。一般来说，汉语中的句子分以下几种： 陈述句：用来说明事实的句子。 祈使句：用来要求听话人做某件事情的句子。 疑问句：用来提出问题的句子。 感叹句：用来抒发某种强烈感情的句子。 复句、分句：意思上有密切联系的小句子组织在一起构成一个大句子。这样的大句子叫复句，复句中的每个小句子叫分句。 构成句子的语言单位是词语，即词和短语（词组）。词即最小的能独立运用的语言单位。短语，即由两个或两个以上的词按一定的语法规则组成的表达一定意义的语言单位，也叫词组。 标点符号是书面语言的有机组成部分，是书面语言不可缺少的辅助工具。它帮助人们确切地表达思想感情和理解书面语言。 二、用法简表 名称 时间前面加的介词in，at，on的区别 【in】我是“大姐”，因为我后面所接的都是较长时间。 具体用法有：1．表示在较长的时间里（如周／月份／季节／年份／世纪等）。如：in a week；in May；in spring／summer／autumn／winter；in 2008；in the 1990’s等。 2．表示在上午、下午或晚上。如：in the morning／afternoon／evening。 3．in the daytime（在白天）属于固定搭配，指从日出到日落这一段时间4．“in ＋一段时间”表示“多久以后／以内”，常与将来时连用。如：in half an hour；in ten minutes；in a few days等。 【on】我是“二姐”，我后面所接的时间多与日期有关。 具体用法有：1．表示在具体的某一天（如日期、生日、节日或星期几）。如：on May 4th，1919；on Monday；on Teachers’ Day；on my birthday；on that day等。 2．表示某一天的上午、下午或晚上。如：on the morning of July 2；on Sunday afternoon；on a cold winter evening等。 【at】我是“小妹”，因为接在我后面的时间最短。 具体用法有：1．表示在某一具体时刻，即几点几分。如：at six o’clock；at half past nine；at a quarter to six；at this time等。 2．表示在某一短暂的时间。可指某个节日或被认为是一年中标志大事的日子如：at noon；at this moment；at the end of a year；at the start of the concert，at New Year, at Christmas等。 练习： ( ) 1. Children get gifts ____ Christmas and ____ their birthdays. A. on; on B. at; on C. in; in D. in; on ( ) is nothing ____tomorrow afternoon, is there -----No. We can have a game of table tennis. 时间介词(at, in ,on) 的用法与练习 【时间介词记法口诀】: at用在时刻前，亦与正午、午夜连， 黎明、终止和开端，at与之紧接着相伴。 周月季年长时间，in须放在其前面， 泛指一晌和傍晚，也要放在in后边。 on指特定某一天，日期、星期和节日前 某天上下和夜晚，依然要在on后站。 今明昨天前后天，上下这那每之前， at、in、on都不用，此乃习惯记心间。 1. at+night/noon/dawn/daybreak/点钟（所指的时间小于天）： at night( ) at noon( ) at down( ) at daybreak( ) at7:30( ) at 7o’clock ( ) 2. in+年/月/季节/泛指某一天的上morning，下afternoon，晚evening（所指时间大于天）： in 2004（）in March（）in spring（） in the morning（）in the evening （）in the afternoon（） 扩展：在一段时间之后。一般情况下，用于将来时，意为“在……以后”。如：He will come in two hours. 3. on+星期/日期/节日/特指某一天的上，下，晚（所指时间是天）： on Sunday（）on May 4th( )on Sunday morning( ) on Christmas Day( )/on Teachers’ Day( ) on the morning of Sunday( ) on a cold winter morning( ) 扩展：准时，按时。如： on time 按时，in time 准时 练习 一、用介词in on at填空 ______1999 _______9:45 _______the evening _______Monday evening ________June ________the afternoon _______noon ______night ______Children’s Dayin on at的时间用法和地点用法 完全版
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