a r X i v :h e p -t h /0104202v 2 18 J u l 2001February 1,2008hep-th/0104202
HUTP-01/A019
Duality of the Fermionic 2d Black Hole and N =2Liouville
Theory as Mirror Symmetry
Kentaro Hori and Anton Kapustin Je?erson Physical Laboratory School of Natural Sciences Harvard University Institute for Advanced Study Cambridge,MA 02138,U.S.A.Princeton,NJ 08540,U.S.A.Abstract We prove the equivalence of the SL (2,R )/U (1)Kazama-Suzuki model,which is a fermionic generalization of the 2d Black Hole,and N =2Liou-ville theory.We show that this duality is an example of mirror symmetry.The essential part of the derivation is to realize the fermionic 2d Black Hole as the low energy limit of a gauged linear sigma-model.Liouville theory is obtained by dualizing the charged scalar ?elds and taking into account the vortex-instanton e?ects,as proposed recently in non-dilatonic models.The gauged linear sigma-model we study has many useful generalizations which
we brie?y discuss.In particular,we show how to construct a variety of dila-tonic superstring backgrounds which generalize the fermionic 2d Black Hole and admit a mirror description in terms of Toda-like theories.
1Introduction
The mirror dual of an N=2supersymmetric non-linear sigma-model on a toric variety has been derived in[1]by realizing the model as the low energy limit of a gauged linear sigma-model[2],and dualizing the phases of charged scalar?elds.This can be viewed as T-duality applied to the?bers of a torus?bration.When a circle?ber shrinks to zero size at some locus of the base,one could na¨?vely expect that the dual circle blows up at the same locus.What really happens is the following.To each such degenerating?ber there corresponds a superpotential term,generated by the vortex-instanton of the gauge system (analogously to[3]),that diverges toward the degeneration locus.The superpotential also breaks the rotational symmetry of the dual theory,accounting for the loss of winding number in the original system due to the degeneration of the circle.This is the story for(2,2)supersymmetric non-dilatonic sigma-models on toric manifolds,but it would be interesting to see how universal this phenomenon is.
Some time ago,Fateev,Zamolodchikov and Zamolodchikov(FZZ)[4]conjectured a duality between the conformal?eld theory of a two-dimensional Euclidean black hole[5] and a Landau-Ginzburg theory,called sine-Liouville theory.The2d Black Hole is de?ned as the level k SL(2,R)/U(1)coset model and has the following target-space metric and dilaton for large k
d s2=k[dρ2+tanh2ρd?2],
Φ=Φ0?2log coshρ.(1.1) Here?is a periodic variable of period2π.The coset theory is well-de?ned for all k>2. On the other hand,the sine-Liouville theory is a theory of scalar?elds?∞
S=1k?2(d?)2+1k?2R h?+μ2e??cos? √
k and the dilaton is linear,Φ～?2ρ.Atρ=0the circle shrinks to zero size,and therefore the overall geometry is that of a semi-in?nite cigar.Sine-Liouville
theory also has an asymptotic region,?→∞,where the potential is exponentially small
√
and the theory is the sigma-model on a cylinder of radius1/
therefore for small k,where the radius of the cylinder is large and semiclassical reasoning is valid,we expect the model to be unstable.This corresponds to the fact that the coset model is well-de?ned only for k>2.
If we compare the radii of the two asymptotic regions,we notice that the two theories may be related by T-duality.The shrinking of the circle as one goes towardsρ=0on the2d Black Hole side corresponds to the exponentially growing potential which breaks rotational symmetry on the sine-Liouville side.Thus FZZ duality is strongly reminis-cent of mirror duality between(2,2)sigma-models and(2,2)Landau-Ginzburg models mentioned above.
In this paper,we prove the supersymmetric version of FZZ duality using the method of [1].Instead of a2d Black Hole we consider a fermionic2d Black Hole,de?ned as the level k SL(2,R)/U(1)Kazama-Suzuki supercoset model[7],and instead of sine-Lioville theory we consider N=2supersymmetric Liouville theory[8].This duality was conjectured in [9]from the space-time point of view;closely related ideas were discussed earlier in[10–12], and the duality was studied more recently in[13].The supercoset model can be viewed as an N=1supersymmetric sigma-model with target-space metric(1.1).The action for N=2Liouville theory on a?at world-sheet is given by
S=12k|Y|2+1
2π d2x d4θ 4(P+2e2|Σ|2 .(1.4)
We will?rst give some numerical evidence.We will show that the sigma-model that arises after integrating out the gauge multiplet?ows under one-loop renormalization group?ow to the supersymmetric sigma-model with target-space metric(1.1).We will explicitly see how the linear dilaton in the asymptotic region is generated.The one-loop approximation
is valid for large k.To go beyond this approximation,we compute the infrared central charge of the above gauged linear sigma-model(GLSM).Following[14,15],we identify the right-moving N=2superconformal algebra in the ring of left-chiral operators.The classical gauge theory(1.4)has both vector and axial R-symmetries,but on the quantum level the axial R-symmetry is anomalously broken.However,one can modify the current using the?eld P to make it conserved.This allows us to identify the right-moving R-current,and then the full N=2superconformal algebra.The correction terms in the superconformal currents are linear in P and generate linear dilaton in the asymptotic region.(Alternatively,one can obtain the whole current super?eld by cancelling the Konishi anomaly[16]associated to the axial anomaly.)We?nd that the central charge is
c=3 1+2
(this can be derived either by
4k
using the fact that the supercoset is asymptotic to a linear dilaton theory with back-
√
ground charge Q=1/
1We assume that world-sheet parity is a symmetry of the theory.Otherwise h min is de?ned as the smaller of the lower boundaries of the spectra of L0and?L0.
generalization of[1].Dualizing the phase ofΦand the imaginary part of P,we obtain twisted chiral super?elds Y and Y P of period2πi.The superpotential of the dual system is
W=Σ(Y+Y P)+μe?Y,(1.6) where the term linear inΣis present already at the classical level,and the exponential term is generated by the vortex ofΦ.Note that the P-vortex is absent,and therefore no nonperturbative superpotential is generated for Y P.The K¨a hler potential is
K=?1
2k|Y P|2+...,(1.7)
where dots denote a possible correction term that vanishes in the asymptotic region Re Y→∞.In the infrared limit e→∞it is appropriate to integrate outΣ,and this gives a constraint Y+Y P=0.Thus,we obtain a theory of a single periodic chiral super?eld Y with the superpotential e?https://www.doczj.com/doc/f618993036.html,ing the uniqueness of the supersymmetric coset,one can show that the corrections to the K¨a hler potential indicated by dots in(1.7) are in fact absent.Note that in general the methods of[1]do not allow to control the K¨a hler potential.What makes the present case di?erent is that one can continuously deform the gauge theory(1.4)to the N=2Liouville theory without breaking any sym-metries.Since the supersymmetric coset is rigid,this implies that the infrared limit of the theory(1.4)is equivalent to N=2Liouville theory.This alternative way of deriving the mirror dual is less general than that used in[1],but provides more information about the dual theory.
We also describe some obvious generalizations of the model(1.4),compute their in-frared central charge and?nd mirror duals.Some of these models?ow to non-trivial(2,2) superconformal?eld theories and can be used to construct a variety of higher-dimensional superstring backgrounds with a non-constant dilaton and fermionic symmetries.Others are massive?eld theories which upon integrating out the gauge?elds reduce to sigma-models on“squashed”toric varieties.Mirror symmetry relates these sigma-models to Landau-Ginzburg models;for example,the sigma-model on a“squashed”CP1(the su-persymmetric“sausage model”)is mirror to the N=2sine-Gordon model with a?nite K¨a hler potential.In fact,in this particular case both theories are integrable,and their equivalence has been conjectured by Fendley and Intriligator[21].(The squashed toric sigma models and the mirrors are also introduced and studied from a di?erent but related point of view in[22].)
2The Gauged Linear Sigma-Model
The ?eld content of the gauged linear sigma-model will be the following:two chiral super?elds Φand P and a vector super?eld V .Our super?eld conventions are collected in Appendix A.The gauge transformations laws are de?ned to be
Φ→e i ΛΦ,
P →P +i Λ,
V →V ?i Λ+i
D +Λ=
2π d 2x d 4θ 4(P +2e 2|Σ|2 .(2.2)
Here Σ=
D +Σ=D ?Σ=0.We did not include the Fayet-Iliopoulos term as it can be absorbed into P .Neither did we include its superpart-ner,the theta-angle,since it breaks world-sheet parity,while we want the theory to ?ow to a parity-invariant supercoset model (see Appendix D for details about the de?nition of world-sheet parity for the coset models).
The chiral super?eld P can be gauged away completely,after which one is left with Φand a massive vector super?eld described by V .Thus the action (2.2)describes massive N =2QED.Alternatively,one can choose the Wess-Zumino gauge for V and retain P .Then the action in terms of component ?elds reads
1φD μφ+i ψ+(D 0?D 1)ψ++D |φ|2+|F |2
?|σ|2|φ|2?ψ+φλ?ψ++i ψ+ψ?
2 ?D μχ?(?0+?1)χ?+i p )+|F P |2
?|σ|2+iχ+λ??iχ?λ++i λ??i λ+ +1σ?μσ+i λ+(?0??1)λ++v 201+D 2 .(2.3)
Here φand p are the lowest components of Φand P ,respectively,ψand χare their superpartners,and v μ,λ,and D are components of a vector multiplet in the Wess-Zumino gauge.D μφand D μψ±are the standard covariant derivatives,while D μp :=?μp +iv μ.
After one gauges away the imaginary part of p,one can see that the gauge?eld and its superpartners have mass e
√
k one can integrate outΣand set the D-term potential to zero.The D-term is given by
D(φ,p)=|φ|2+k Re p.
To obtain the low-energy e?ective action forΦwe set Im p=0(this is a gauge choice), express Re p in terms ofφby means of D(φ,p)=0,and integrate out V omitting the last term in the action(because the infrared limit is equivalent to taking e→∞).Equiva-lently,we can take the?at space parametrized byφand p with K¨a hler potential
K(φ,p)=|φ|2+
k
k )dr2+
r2
k
dθ2.(2.4)
Here r=
√
k. Thus it describes a cigar,i.e.a2d Riemannian manifold di?eomorphic to R2with a metric which has a U(1)isometry and asymptotes to a?at metric on a cylinder.
The metric(2.4)is di?erent from the usual2d Black Hole metric[5].If one sets r=
√
gρρ(ρ)dρ.(2.7)
In terms of v,θany cigar-like metric has the form
ds2=dv2+F2(v)dθ2
for some function F(v)which approaches a constant for v→∞.For our metric the di?er-√
ence F(v)?
R ij.(3.1)
2π
Its only zero is a?at metric,and since any cigar has a nonzero curvature near the tip, na¨?vely it appears that a cigar-like metric cannot be a?xed point of the RG?ow.The
resolution of this puzzle is well-known(see e.g.[23])and is related to the possibility of having a dilaton gradient.In the usual formulation,the dilaton a?ects the coupling of the sigma-model to a curved world-sheet metric.Alternatively,if one prefers to stay on a?at world-sheet,one may say that a non-trivial dilaton gradient in space-time is equivalent to assigning a non-trivial Weyl transformation law to target-space coordinates.
Once the possibility of a non-trivial Weyl transformation law for X i is recognized, it is easy to see in what sense a cigar can be invariant under RG?ow.Let us?x a conformally-?at gauge for the space-time metric G ij,so that it has the form
ds2=eΨ(u) du2+dθ2 .(3.2) The functionΨ(u)does not depend onθbecause we are only interested in the sigma-models which have a U(1)isometry.The tip of the cigar corresponds to u→?∞,while the cylindrical asymptotics is reached for u→+∞.From the known behavior at the tip and at in?nity we infer that
Ψ(u)～2u+...for u→?∞,(3.3)
Ψ(u)～log k+...for u→+∞.
The functionsΨ(u)and F(v)are related as follows:
F(v)=eΨ(u)/2,v= u?∞eΨ(u)/2du.(3.4)
Note that both(3.2)and(3.3)are left invariant by reparametrizations u→u+c,θ→θ+c′,where c,c′are constants.This is what remains of reparametrization invariance after we?x the gauge(3.2,3.3).Hence the most general transformation law for u andθunder the Weyl rescaling of the world-sheet metric by t2is
u→u+at,θ→θ+a′t,
where a,a′are real constants.Saying that the metric approaches a?xed limit under such a modi?ed Weyl transformation is equivalent to saying that forμ→∞the function Ψ(u,t)depends only on the di?erence u?at:
Ψ(u,t)→ΨIR(u?at).
SinceΨdoes not depend onθ,by a t-dependent reparametrization ofθone can make a′=0.
The one-loop RG equation forΨis
?Ψ(u,t)
4πe?Ψ(u,t)
?2Ψ(u,t)
4π
e?ΨIR(u)Ψ′′IR(u)+aΨ′IR(u)=0. The general solution of this equation is
eΨIR(u)=
1
λ
,
whereλ,b are constants.Imposing the conditions(3.3),we obtain
λ=2,a=
1
e?2(u?b)+1 k tanhρ=eΨIR(u)/2
the metric
ds2=eΨIR(u)(du2+dθ2)
is transformed to the form Eq.(2.6).This proves that the only cigar-like?xed point of the one-loop RG equations is the2d Black Hole.
We now would like to show that our metric(2.5)indeed?ows to this infrared?xed point.We set
Ψ(u,t)=f(u?t/(2πk),t),
and solve numerically the RG equation for f(u,t).The initial condition is implicitly given by the metric(2.5).Explicitly,Ψ(u,0)=Ψ0(u)can be written in a parametric form
eΨ0(u(r))=kr2
2
.
It is useful to note that the equation(3.5)is invariant with respect to the transforma-tion
Ψ(u,t)→Ψ(u,t)+log q,t→qt.
This means that we can absorb k into the de?ntion of the RG time t.Therefore in the remainder of this section we set k=1.
v
0.900.951.00F v,t tanh v
Τ 0
Τ 1
Τ 4
Τ 20
Τ 200
Figure 1:RG evolution of the cigar metric.We plotted F (v,t )/tanh v as a function of v for several values of the rescaled RG time τ=t/(4π).
For numerical integration we used an implicit scheme,which requires solving a sparse (tri-diagonal)system of linear equations at each step (see e.g.[24]).It is also convenient to reparametrize the variable u so that it runs over a ?nite rather than an in?nite interval.The results of the numerical integration of the RG equation are presented in Figure 1.We chose to plot the ratio F (v,t )/tanh v where F (v,t )is related to Ψ(u,t )by (3.4).For the 2d Black Hole this ratio is equal to 1.From Figure 1it is evident that F (v,t )/tanh v approaches 1as t →+∞.Hence at one-loop level the sigma-model with target-space metric (2.5)?ows to the 2d Black Hole (2.6).
The discussion in this section clari?es how a linear dilaton is generated by the RG ?ow.The point is simply that as the RG time increases,the cigar tries to shrink,so that its tip moves towards positive u .In order to “keep up”with the tip,one has to make a t -dependent reparametrization of the u -coordinate,which is equivalent to rede?ning the Weyl transformation law for u .
4An Exact Computation of the Central Charge
In the previous section we have analyzed the renormalization group ?ow in the one-loop approximation which is valid for large k .In this section,using the method of [14,15],we show that the central charge of the IR superconformal ?xed point has to be exactly c =3+6/k .This computation is used in the next section to prove that the GLSM (2.2)?ows to the fermionic 2d Black Hole for all k >0.
4.1
Q+.It is a nilpo-tent operator whose anti-commutator with its conjugate Q+is the left-moving translation operator:
(Q+,Q+}=H+P.(4.1) By the nilpotency,one can consider
Q+,O]=0then [H+P,O]={Q+-closed operators are independent of x+=x0+x1,that is,they depend only on the x?=x0?x1coordinates of the insertion points.(In the Euclidean theory they are holomorphic functions.)In particular they form a right-moving operator product algebra(i.e.a chiral algebra).
Suppose a(2,2)?eld theory?ows to a(2,2)superconformal?eld theory.Then(2,2) supersymmetry is enhanced in the IR limit to left-moving and right-moving N=2super-Virasoro algebras whose generators(anti-)commute with each other.In particular,the right-moving super-Virasoro is contained in the chiral algebra of
Q+-cohomology at?nite energy).Therefore,if one can uniquely identify such a chiral algebra at?nite energy,one can learn about the right-moving superconformal algebra in the IR limit,and in particular compute its central charge.
So let us look for such a superconformal algebra in the
D+J=0.(4.2) Then the lowest term in theθ+,
Q+,J|
θ+=
D+=Q+cohomology class.Its lowest component will?ow to the right-moving R-current of the IR theory
(modulo
ψ?ψ?+k χ?χ??1λ?λ?,
(4.4)j ±A =±ψ?
2χ?2e 2λ?
e 2(??σ??σ).(4.5)The right-moving R-current j ±R =1ψ?+
k χ?+i σσ?2e 22e 2(?+σ?+σ).(4.7)
In the limit e 2→∞where the Σmultiplet becomes very massive,j ?R vanishes and j +R
obeys the right-moving condition ?+j +R =0classically.Let us consider a super?eld
J ?=D ?(Φe V )e ?V
Φ)+k P +V )P +V )+i Σ.(4.8)
It is invariant under the gauge transformation (2.1),and its lowest component ψ?2χ?e 2
σ?D +Φ)=0,
(4.9)D ?(P +
Φ+k P +V )+1D ?Σ+D ?Σ)=0,(4.11)
it is easy to check that this super?eld obeys the right-chiral condition
D +J ?=1D ?Σ.(4.12)
This is a supersymmetric extension of the chiral anomaly equation
?μj μA =2F +?.(4.13)
The factor 2in front of F +?can be understood by noting that there are n zero modes for both ψ?and 2π
F .The equation (4.12)is a (1+1)-dimensional version of the Konishi anomaly [16],and its detailed derivation is given in Appendix C.
Usually,the anomalous current cannot be modi?ed in a gauge-invariant way so that it is conserved.The situation is di?erent in the present theory where we have a ?eld ?P :=Im p that shifts under the gauge transformation.Then,the curvature F +?can be expressed as a di?erential of a gauge invariant quantity
A μ=?μ?P +v μ,
(4.14)
namely F +?=?+v ????v +=?+A ????A +.Then the modi?ed axial current
j +A =j +A ?2A ?, j ?A =j ?A +2A +,is gauge-invariant and conserved.This story has a supersymmetric generalization.Letting
δJ =1D ?D ??D ?
P +V ),(4.15)we can derive from (4.10)that D ?Σ.This is correct quantum mechani-cally,since the equation of motion (4.10)is used linearly.Thus the modi?ed current
J :=J ?+δJ
(4.16)satis?es the right-chiral condition on the quantum level:θ±=0=ψ?2
χ?e 2σ??
ψ?+k χ?+i σ +??
1λ+λ+?i σ?+σ =F +?=2?+A ?,(4.19)
where we have used the ?P equation of motion ?μA μ=0in the last step.We note that
σ?+σ={σψ?+k χ?+i σ?2A ? =0modulo {
4.3The superconformal algebra
We de?ne the currents j ?,G ?,
D ?J ,1D ?,D ?]J .They have the following expressions in terms of
component ?elds:
j ?=ψ?2χ?e 2σ??
p ),(4.21)G ?=?2iψ?D ?p +
1λ?+i??χ?,(4.22)ψ?+ki D ?p e 2
λ???χ?,(4.23)T ?=2D ?φD ?
p +1
σ?σ?2?2
(ψ?D ?ψ?)+ik χ????χ?2e 2λ???
2??(D ?p +D ?p ).)The quadratic terms
in the currents come from J ?,and the linear terms are from the “quantum correction”δJ .Since they are the lowest components of right-chiral super?elds,they represent right-moving
ψ?(x )ψ?
4χ?χ?(0)?1σ(x )σ??(x ?)2+k 2
(x ?)2
?1(x ?)2+4?1/2k (x ?)2.(4.25)Similarly,we can show that the rest of the OPE has the form j ?(x )G ?(0)～
?i G ?(0)～i G ?(0),T ?(x )j ?(0)～
?1x ???j ?(0),T ?(x )G ?(0)～
?3/2x ???G ?(0),T ?(x )(x ?)2x ???
2(x ?)4+?2x ???T ?(0),
G ?(x )(x ?)3?2
x ? T ?(0)?i
This is an N=2superconformal algebra with central charge
c=3 1+2
D?(P+
D+J2=0by virtue of the equations of motion(4.10).1This current is free of Konishi anomaly or
D+J2=0is derived by using the equation of motion linearly.Thus it appears that one can modify the current J by an arbitrary multiple of J2
J′=J+a J2.(4.30) It is easy to see that the four currents j′?,G′?,
ψ?+k
χ?+
i
σ+i(D?p?D?p,
=Re j′?+i 1
1The chiral current for the phase rotation ofΦis D?Φ).This is equal to?k D?(P+ D+(i??D?
D+exact terms.
The current in the infrared limit has to be real and therefore the imaginary part in (4.31)has to vanish up to
??|σ|2is negligible
2e2
in that region,becauseσhas a large mass due to large values of|φ|2～?Re p/2.On the other hand,the?eld??Re p survives in the IR limit as a free?eld(possibly with a background charge),and is not Q+-exact terms,we have to set
a=0.(4.32) It follows that j?,G?,
k .(5.1) Unlike in the bosonic case,here the expansion of the central charge in powers of1/k terminates at one-loop order.For large k this CFT is weakly coupled and is equivalent to the sigma-model with target(2.6).Note that the central charge of the fermionic2d Black Hole at level k is exactly the same as the IR central charge of the GLSM(2.2)
computed in Section4.In the asymptotic region of the target space both models become
√
equivalent to the theory of a free chiral super?eld with radius
clear from the fact that the sigma-model metric(1.1)describing the supercoset has a U(1) isometry which shifts?).Thus the supercoset has the same symmetries as the IR?xed point of the GLSM.
The analysis of Section3shows that for k→∞the GLSM(2.2)?ows to the fermionic 2d Black Hole at level k.For?nite k we only know that the GLSM?ows to a(2,2) superconformal?eld theory with the same central charge,symmetries,and asymptotic behavior as the fermionic2d Black Hole at level k.It could be that for?nite k the GLSM ?ows not to the supercoset,but to some other?xed point nearby.But if this is the case, then the supercoset theory must admit a marginal operator which deforms it to the IR ?xed point to which the GLSM?ows to.This operator must preserve all the symmetries of the2d Black Hole and leave its asymptotic behavior unchanged.If we can show that such marginal operators are absent,then the GLSM(2.2)has no choice but to?ow to the fermionic2d Black Hole for all k>0.
5.2Marginal deformations of the bosonic coset
As a warm-up,let us discuss marginal deformations of the bosonic SL(2,R)/U(1) coset.This problem has been previously addressed in[25,26].We will focus on marginal deformations which preserve all the obvious symmetries of the coset,i.e.momentum and world-sheet parity.In addition we require the deformation to decay or stay constant towardsρ→∞,so that the asymptotic behavior of the model is not drastically altered.
First,let us consider marginal operators in the coset which correspond to normalizable states in the parent WZW theory.The quantization of the SL(2,R)WZW has been a subject of interest for many years,but the precise spectrum of the theory was determined only recently[27].According to[27],one should include the following representations of SL(2,R)as the Kac-Moody primaries:
.
(i)D+j:principal discrete representation with lowest weight of spin j,1
2
.
(ii)D?j:principal discrete representation with highest weight of spin?j,1
2 (iii)Cαj:principal continuous representations with j=1
sentations by D±j, Cαj.However,one should also include other representations labeled by an integer w[27].These are obtained by declaring that the primary is annihilated by J+n+w,J3n,and J?n?w for n>0.One says that these new representations are obtained from the usual positive-energy representations by the spectral?ow.They are denoted by D±,w j and Cα,w j.Under the spectral?ow by w units,the L0and J30eigenvalues of a state change as(h,m)→(h+wm?kw2/4,m?kw/2).In general spectral?ow takes a positive-energy representation of
SL(2,R)to a representation with energy unbounded from below.The exceptions to this rule are D+,w=?1j and D?,w=1j.They are equivalent to D?k2?j, respectively.More generally,we have
D?,w j? D+,w?1k
2
,w∈Z)and Cα,w j× Cα,w j(j∈1
k?2
.(5.3) After the spectral?ow by w its quantum numbers become
J30=m?kw
2
,(5.4)
L0=?j(j?1)
4
,?L0=?
j(j?1)
4
.(5.5)
States of the coset theory are represented by states of the parent WZW theory obeying
J30+?J30=0,(5.6)
J3n=?J3n=0,n≥1.(5.7) The momentum in the coset theory is given by
J30??J30.
The Virasoro generators are represented by L n?L U(1)n,?L n??L U(1)n where L U(1)n and?L U(1)n are the Sugawara operators of the U(1)subalgebra at level k.
We are interested in Virasoro primaries in the coset theory which have dimension(1,1) and zero momentum.This means that we are looking for Virasoro primaries of the parent WZW theory satisfying(5.7)together with
J30=?J30=0and L0=?L0=1.(5.8)
A little high-school algebra shows that in the discrete representations there are two such states for k>3:
J??1?J??1|j=1 +,(5.9)
J+0?J+0|j=k
2?1
and D?1and write the second state as1
J+?1?J+?1|j=1 ?.(5.11) Since world-sheet parity exchanges J±and?J?and D+j× D+j and D?j× D?j(see Appendix D),the statement becomes obvious.
The above two states are in the spectrum if1<(k?1)/2,i.e.for k>3.For k=3the states become delta-function normalizable and appear in the continuous representations with j=1/2,α=1/2,w=±1(see below).For2 Thus for k>3there are two marginal operators in the SL(2,R)WZW theory which come from discrete representations and could give rise to marginal momentum-conserving deformations of the coset.It is easy to write down their explicit form.Following[27]we use the coordinates(ρ,t,?)on SL(2,R)de?ned by g=e iσ2(t+?)/2eσ3ρe iσ2(t??)/2(5.12) (φof[27]is replaced here with?to avoid confusion with the scalar component ofΦ). The vertex operators corresponding to the two states in(5.9,5.11)are given by ?+ρcoshρ?i sinhρ??(?t+?) .(5.13) 首届“教育教学技能大比武”总结 为期半个月的青年教师首届“教育教学技能大比武”活动已经圆满落下帷幕。参加本次比赛的教师都是38周岁以下的青年教师，比赛内容包括讲课、答辩、三笔字、演讲四个环节。这次活动在学校领导的大力支持下，在全体教师的努力配合下，在参赛教师积极参与、认真准备下，取得圆满成功。 回顾本次比赛活动，老师们无论是在个人综合素质、教材把握能力还是在课堂驾驭能力上都有精彩的展示，下面对本次活动做一个总结： 一、讲课赛环节 这十九位青年教师对此次比赛高度重视，认真备课、讲课，为我们呈现了一节节风格各异、亮点纷呈的课，主要呈现了一下几个特点： 1、备课充分、设计用心。 老师们在备课过程中，能深入钻研教材，做了大量充分的准备。老师们都精心设计导语，创设情境，千方百计地激发起学生强烈的求知欲，能够把知识和能力深入浅出又扎扎实实的传授给学生，每一节课都朴实无华，每一节课都独具匠心，比如：郑珊老师在讲授《图形的旋转》一课时，教学设计层次分明，抓住平移和旋转的特征明确其描述方法，在新授的过程中能够放手让学生自己思考-动手操作-小组交流-展示（说明描述），老师引导学生亲历学习过程，通过几个有效的追问，使自己体会掌握了学习内容。 2、教学扎实有效，注重基础训练。 老师们能够抓住教学目标，精心设计每一个环节，同时老师们十分注重基础训练，比如高年级语文老师在教学中注重字词的品读与指导，在阅读教学中，老师能通过阅读来领悟文本的内涵，例如王玉英讲述《梅花魂》一课，她更注重引导学生“品词、品句、品读”以此让学生以读明理，以读悟情，通过“品”字让学生真正体会到了外祖父为什么那么珍爱墨梅图，从而理解梅花的品行，上升到中国人的气节。语文中低年级教学中，教师注重字形的书写字文的理解和区别运用，比如赵彤霞老师执教《植物妈妈有办法》一课，能在文中恰到好处的让学生理解“许多”和“许”“多”的区别，并用“纷纷”说一句话。又比如赵志芳执教《秋天的雨》一课中，注重了“爽”字的书写指导，教学中注重句子的训练，让学生练说比喻句。 3、注重学生情感态度和学习习惯的培养。 注重学生情感态度和学习习惯的培养是成为这次比赛课的又一亮点。老师们在教学中，做到自始至终关注学生的情感，营造宽松、民主、和谐的教学气氛，尊重每个学生，积极鼓励他们在学习中的尝试，保护他们的自尊心和积极性。比如吴蕊霞老师的鼓励具有个性化，激励性的语言常挂嘴边，成为学生不断学习、创新不可缺乏的精神动力。同时在教学中注重学习习惯的培养，比如高月枝老师在授课的同时适时对学生进行了课常规的教育，整个一节课，教学秩序井然有序，对于刚上学两个星期的孩子真的很难得。 4、善用多媒体教学。 本次讲课赛几乎所有的老师都制作了精美实用的多媒体课件，追求既生动形象又快捷高效的教学效果。特别是赵丽和龚伟科两位老师用我们上学期培训的知识制作了白板课件。 5、教师素养良好。 通过这次比赛，我们欣喜地看到我校青年教师具备良好的教师基本素质。他们教态大方得体，语言清晰，具有较强的亲和力和应变能力。王敏、陈蓉等老师她们在课堂上文雅得体的教态，丰富的肢体语言以及亲切和蔼的微笑，都给我们留下了深刻的印象，深受学生的喜爱。 针对本次讲课赛反映出的问题，给老师们提出以下建议，跟老师们商榷：1、语文教学中，略读课文的教学教师应大胆放手学生，让学生充分展示自己。有感情的朗读，重在先理解再 Unit 3 单元试题Part I Vocabulary and grammar I. Write out the following countries’ main language. II. Translate the following expressions. 1. tour guide 2. shop assistant 3. apply for 4. oral English 5. keep up 6. 记日记 7. 听起来不错 8. 拜访朋友 9. 把某人介绍给某人 10. 害怕 III. Complete the following sentences with the proper form of the given phrases. used to keep it up apply for it seemed that agree with be over give it a try try to 1. Do you ________________________me? 2. I think _______________________________ and I will find it a lot of fun. 3. When class _____________________, we talked about where to go for dinner. 4. __________________they couldn’t understand each. 5. I ____________________ a job in a big company. 6. He found it very difficult to _____________ every day. 7. My English ________ be poor but now I am good at it. 8. In English class, everyone _____________speak in English. IV. Choose the best answers. ( ) 1. In the USA, most people speak _________. A. America B. English C. England D. American ( ) 2. _______ has the largest number of speakers. A. China B. Chinese C. French D. English ( ) 3. Is English _______ for the job? A. must B. need C. a must D. a need ( ) 4. English keeps _________ all the time. A. change B. changing C. to change D. changed ( ) 5. He spent a lot of time ________ English these days. A. study B. to study C. is studying D. studying ( ) 6. In some Western countries, people try ______a black cat. A. to avoid B. avoid C. avoiding D. avoided Part II Oral practice I. Match the questions with the answers. 1. What is he? A. He is a tour guide. 2. Where is he from? B. He speaks English. The way 的用法 Ⅰ常见用法： 1)the way+ that 2)the way + in which（最为正式的用法） 3)the way + 省略（最为自然的用法） 举例：I like the way in which he talks. I like the way that he talks. I like the way he talks. Ⅱ习惯用法： 在当代美国英语中，the way用作为副词的对格，“the way+ 从句”实际上相当于一个状语从句来修饰整个句子。 1)The way =as I am talking to you just the way I’d talk to my own child. He did not do it the way his friends did. Most fruits are naturally sweet and we can eat them just the way they are—all we have to do is to clean and peel them. 2）The way= according to the way/ judging from the way The way you answer the question, you are an excellent student. The way most people look at you, you’d think trash man is a monster. 3）The way =how/ how much No one can imagine the way he missed her. 4）The way =because 教师即兴演讲题目之63个话题 来源：思雨教育资源网|教学资源|课件论文|作文作者：无边思雨发表日期：2009-5-30 13:16:19 阅读次数： 910 查看权限：普通文章 1、如何维护班集体荣誉？ 2、如何看待学生时代早恋问题？ 3、成人与成才二者是怎样的关系？结合实例说明自己的观点。 4、不同地域、不同背景、不同习惯的同学之间该如何相处？ 5、怎样面对学习、生活中遇到的挫折？ 6、你最崇拜的人是谁？“名人”还是自己？ 7、你认为我们是否应有感恩之心？感恩于谁？ 8、你希望自己会是怎样一位老师？你会如何教育自己的学生？ 9、“言行、仪表”与个人的发展。 10、如今继续提倡“勤俭、节约”作风是否已过时？ 11、在各种资料、媒体中常讲张扬个性，你认为我们该张扬什么样的个性？ 12、三轮车工人方尚礼自己生活的如乞丐，却将自己蹬车收入的35万多元用来资助失学儿童，当病重时，社会捐助给他治病的钱，也被他捐给了希望工程。你对方尚礼的这种行为有何评述？ 13、电视广告不宜过多 14、保护环境是每个人的责任 15、我中学时代的一个朋友 16、世界需要热心肠 17、向权威挑战 18、2008年的我 19、我爱电视广告 20、我的母亲 21、尊重是孩子成长的基石 22、如何培养学生的好奇心 23、推广普通话 24、“恶语伤人六月寒” 25、我心中的偶像 26、假如我是画家 27、童年趣事 28、珍惜现在 29、我最爱看的电视节目 30、有人认为老师是不断燃烧的蜡烛，你认为呢？ 31、新课程背景下良好师生场的营造。 32、让谐趣幽默走进我们的课堂。 33、阅读教学中如何开展有效的对话教学？ 34、如何正确处理价值取向和个性化阅读的关系？ 35、新课程背景下一堂好课的标准是什么？ 36、“语文教学工具性与人文性统一”的内涵是什么？ 37、如何实践语文教学的人文性和工具性的“统一”？ 38、如何挖掘教材资源，准确选点，扎实训练？ The way的用法及其含义（二） 二、the way在句中的语法作用 the way在句中可以作主语、宾语或表语： 1.作主语 The way you are doing it is completely crazy.你这个干法简直发疯。 The way she puts on that accent really irritates me. 她故意操那种口音的样子实在令我恼火。The way she behaved towards him was utterly ruthless. 她对待他真是无情至极。 Words are important, but the way a person stands, folds his or her arms or moves his or her hands can also give us information about his or her feelings. 言语固然重要,但人的站姿,抱臂的方式和手势也回告诉我们他(她)的情感。 2.作宾语 I hate the way she stared at me.我讨厌她盯我看的样子。 We like the way that her hair hangs down.我们喜欢她的头发笔直地垂下来。 You could tell she was foreign by the way she was dressed. 从她的穿著就可以看出她是外国人。 She could not hide her amusement at the way he was dancing. 她见他跳舞的姿势，忍俊不禁。 3.作表语 This is the way the accident happened.这就是事故如何发生的。 Believe it or not, that's the way it is. 信不信由你, 反正事情就是这样。 That's the way I look at it, too. 我也是这么想。 That was the way minority nationalities were treated in old China. 那就是少数民族在旧中 定冠词the的用法： 定冠词the与指示代词this ,that同源,有“那(这)个”的意思,但较弱,可以和一个名词连用,来表示某个或某些特定的人或东西. (1)特指双方都明白的人或物 Take the medicine.把药吃了. (2)上文提到过的人或事 He bought a house.他买了幢房子. I've been to the house.我去过那幢房子. (3)指世界上独一无二的事物 the sun ,the sky ,the moon, the earth (4)单数名词连用表示一类事物 the dollar 美元 the fox 狐狸 或与形容词或分词连用,表示一类人 the rich 富人 the living 生者 (5)用在序数词和形容词最高级,及形容词等前面 Where do you live?你住在哪? I live on the second floor.我住在二楼. That's the very thing I've been looking for.那正是我要找的东西. (6)与复数名词连用,指整个群体 They are the teachers of this school.(指全体教师) They are teachers of this school.(指部分教师) (7)表示所有,相当于物主代词,用在表示身体部位的名词前 She caught me by the arm.她抓住了我的手臂. (8)用在某些有普通名词构成的国家名称,机关团体,阶级等专有名词前 the People's Republic of China 中华人民共和国 the United States 美国 (9)用在表示乐器的名词前 She plays the piano.她会弹钢琴. (10)用在姓氏的复数名词之前,表示一家人 the Greens 格林一家人(或格林夫妇) (11)用在惯用语中 in the day, in the morning... the day before yesterday, the next morning... in the sky... in the dark... in the end... on the whole, by the way... Have a Positive Attitude in Life After reading this story, I really shocked by what the man had done. He is a murderer who cruelly killed a black cat loved by his wife, then brutishly murdered his wife instead of his second cat, and hid her carcass in the wall. I was confused with the behavior of the man who did all that damn things. I think this man is abnormal, and it is terrible to live with such a person who has something wrong with his mind. I just wonder how can once a righteous and kind man turned out to be so merciless and why the author wanted to show the ugly aspect of human being. After doing some reading about the author, I found the main character in the story is almost the duplicate of author himself; he expressed his own feelings and thoughts through writing. The author lost his parents when he was very young, and he lacked of warm and parental care and sense of security during childhood. What’s more, there’s nobody for him to confess his sufferings and unhappiness, what he could do is to immerse him in alcohol to escape from the anguish. So the reasons were clear for the conversion of the man’s personality. Firstly, is the outside environment: He was always haunting in the bar and was alcoholic, which shows that his life is aimless and disordered. As a result, he was under control of alcohol. Though the surroundings are vital to one’s character development, but it’s not all. In the story, every time when the man did evil things, he blamed them on the alcohol and others. In my perspective, it was just his excuse to avoid the responsibility. As a human, you can’t give way to the madness; instead, you can have strong will to overcome it. Secondly, plenty of negative emotions such as jealousy, violence, irritation make the man envies to the black cat that was loved by his wife and he is violent and angry to the cat in that the cat was so close to the man that the man felt troublesome. When you have such complicated psychology, the most effective and useful way is to talk with your friends or relatives, but not bury deeply in heart, which will later result in vicious cycle. In a word, both inside and outside reasons lead the man to the depth of sin. He seemed accustomed to perform this crime that he had not felt shameful. So after killing the first cat, he acquired some kinds of satisfaction, which later made him tend to abuse things that he didn’t like and eventually killed his wife. So I draw a conclusion from this story: you should find ways to release your dissatisfactions encountered in lif e; don’t find any excuse s to get you away from punishing or it will lead you to crime abyss. Though environment is influential to one’s mood, you should keep a positive and opportunistic attitude toward life. Only in this way, you can drive all the devils away and lead a cozy and comfortable life. “tｈｅwａｙ+从句”结构的意义及用法 首先让我们来看下面这个句子: Ｒead the foｌloｗｉnｇpassagｅａnd talkａbout ｉt wi ｔh your classmaｔes．Try tｏｔeｌl whaｔyｏu thiｎk ｏf Tom aｎd ｏｆｔhe ｗay the chiｌｄrenｔrｅated ｈim. 在这个句子中，ｔhe waｙ是先行词,后面是省略了关系副词that或in whｉch的定语从句。 下面我们将叙述“the ｗaｙ+从句”结构的用法。 1.tｈe wａy之后，引导定语从句的关系词是tｈat而不是hoｗ,因此，<<现代英语惯用法词典＞＞中所给出的下面两个句子是错误的：Ｔhｉs is ｔｈeｗayｈowｉtｈａppened. This is the way how he ａlwａｙs treats me. 2．在正式语体中,thaｔ可被in which所代替;在非正式语体中，ｔhat则往往省略。由此我们得到theｗay后接定语从句时的三种模式：1) tｈe ｗaｙ＋ｔhａt-从句２）the way +ｉn whiｃh－从句3) the ｗay +从句 例如：Ｔｈe way(in whiｃh ，thａt) ｔhｅｓｅｃomｒade ｓloｏｋａｔｐrobｌems is wrong．这些同志看问题的方法 不对。 Ｔｈｅｗａy(that ,ｉn ｗhiｃh)yoｕ’ｒe doinｇit is comple ｔeｌy crａzy.你这么个干法,简直发疯。 Wｅａdmiｒｅd him for thｅｗay ｉｎｗhｉch he fａｃeｓdiｆficultieｓ． Waｌlａｃe ａｎd Ｄarwiｎｇreed ｏn the way ｉｎwhi ｃh ｄｉfｆｅrｅnt forms ｏf life had ｂegｕn.华莱士和达尔文对不同类型的生物是如何起源的持相同的观点。 Thｉs is ｔｈe ｗaｙ（tｈａｔ) hｅdｉd it. I lｉkeｄｔhe waｙ(ｔhat) ｓｈeｏｒganized ｔhe ｍeetｉng． 3.theｗay(tｈat)有时可以与hｏw(作“如何”解）通用。例如： That’s tｈe ｗaｙ(tｈaｔ) shｅspoke. = Tｈat’s how shｅspoke. The Black Cat Edgar Allan Poe 1FOR the most wild, yet most homely narrative which I am about to pen, I neither expect nor solicit belief. Mad indeed would I be to expect it, in a case where my very senses reject their own evidence. Yet, mad am I not -- and very surely do I not dream. But to-morrow I die, and to-day I would unburthen my soul. My immediate purpose is to place before the world, plainly, succinctly, and without comment, a series of mere household events. In their consequences, these events have terrified -- have tortured -- have destroyed me. Yet I will not attempt to expound them. To me, they have presented little but Horror -- to many they will seem less terrible than barroques. Hereafter, perhaps, some intellect may be found which will reduce my phantasm to the common-place -- some intellect more calm, more logical, and far less excitable than my own, which will perceive, in the circumstances I detail with awe, nothing more than an ordinary succession of very natural causes and effects. 2From my infancy I was noted for the docility and humanity of my disposition. My tenderness of heart was even so conspicuous as to make me the jest of my companions. I was especially fond of animals, and was indulged by my parents with a great variety of pets. With these I spent most of my time, and never was so happy as when feeding and caressing them. This peculiarity of character grew with my growth, and, in my manhood, I derived from it one of my principal sources of pleasure. To those who have cherished an affection for a faithful and sagacious dog, I need hardly be at the trouble of explaining the nature or the intensity of the gratification thus derivable. There is something in the unselfish and self- 黑猫 埃德加·爱伦·坡homely adj.平凡的；朴素的 unburthen vt. 使……安生succinctly adv.简洁地 expound vt.解释；阐述baroque n.巴洛克作品，这里指「奇谈」phantasm n.幻象；幻觉 succession n.继承顺序，自然演替 docility n.温驯 humanity n.仁爱；人道disposition n.性情；性格；气质 conspicuous adj.显眼的jest n.笑话；笑柄 caress vt.爱抚；抚摸sagacious adj.聪明的；精 明的 gratification n.满足；满意derivable adj.可引出的；可诱导的 - 1 - 表示“方式”、“方法”，注意以下用法： 1.表示用某种方法或按某种方式，通常用介词in(此介词有时可省略)。如： Do it (in) your own way. 按你自己的方法做吧。 Please do not talk (in) that way. 请不要那样说。 2.表示做某事的方式或方法，其后可接不定式或of doing sth。 如： It’s the best way of studying [to study] English. 这是学习英语的最好方法。 There are different ways to do [of doing] it. 做这事有不同的办法。 3.其后通常可直接跟一个定语从句(不用任何引导词)，也可跟由that 或in which 引导的定语从句，但是其后的从句不能由how 来引导。如： 我不喜欢他说话的态度。 正：I don’t like the way he spoke. 正：I don’t like the way that he spoke. 正：I don’t like the way in which he spoke. 误：I don’t like the way how he spoke. 4.注意以下各句the way 的用法： That’s the way (=how) he spoke. 那就是他说话的方式。 Nobody else loves you the way(=as) I do. 没有人像我这样爱你。 The way (=According as) you are studying now, you won’tmake much progress. 根据你现在学习情况来看，你不会有多大的进步。 2007年陕西省高考英语中有这样一道单项填空题： ——I think he is taking an active part insocial work. ——I agree with you_____. A、in a way B、on the way C、by the way D、in the way 此题答案选A。要想弄清为什么选A，而不选其他几项，则要弄清选项中含way的四个短语的不同意义和用法，下面我们就对此作一归纳和小结。 一、in a way的用法 表示：在一定程度上，从某方面说。如： In a way he was right.在某种程度上他是对的。注：in a way也可说成in one way。 二、on the way的用法 1、表示：即将来(去)，就要来(去)。如： Spring is on the way.春天快到了。 I'd better be on my way soon.我最好还是快点儿走。 Radio forecasts said a sixth-grade wind was on the way.无线电预报说将有六级大风。 2、表示：在路上，在行进中。如： He stopped for breakfast on the way.他中途停下吃早点。 We had some good laughs on the way.我们在路上好好笑了一阵子。 3、表示：(婴儿)尚未出生。如： She has two children with another one on the way.她有两个孩子，现在还怀着一个。 She's got five children，and another one is on the way.她已经有5个孩子了，另一个又快生了。 三、by the way的用法 青年教师朗诵比赛活动方案 （2014----2015）学年度下学期 一、活动目的： 学校是推广普通话，规范语言文字的主阵地，教师作为推广普通话的中坚力量有着不可忽视的重要作用。因此，为了加强教师基本功训练，提升教师的朗读水平，教导处根据语言文字规范化活动计划，开展以“朗读美文展我风采”的教师朗诵比赛。通过教师美文朗读比赛，提高我校青年教师普通话水平，营造浓厚的校园读书氛围，提升教师教学基本功，促使教师重视朗读教学，促进学生健康和谐发展。 二、活动组织：教导处 三、具体活动安排： 1、培训时间：6月8日（周一）下午14:30 2、比赛时间：6月15日（周一）下午14:30 3、比赛地点：四楼舞蹈室 4、参赛人员：35岁以下（含35岁）青年教师必须参加，同时欢迎35岁以上教师参加。 5、比赛内容：作品自选，体裁不限（不少于三分钟） 6、比赛形式：可配乐，参赛人员独立诵读。 7、评委：黄冬梅蒋丽丽郭艳华贺芳刘忠霞冷静武玉德 8、分数统计：王辉赵慧贤 9、主持：徐金凤 四、活动程序： 1、学校将在赛前一周邀请校长对参赛人员进行培训。 2、参赛教师提前十分钟到达比赛场地，做好准备工作。 3、14:40正式进行比赛，按抽签顺序进行。 4、评分办法：比赛采取现场评分的办法，满分10分，比赛结束后，进行分数汇总、统计，取平均分，宣布比赛成绩。 5、校长点评并作总结。 五、设奖情况： 本次比赛将设一等奖2名，二等奖3名，三等奖5名，优秀奖若干名。比赛成绩计入年末教师量化考核。 六、朗诵比赛评分标准 （一）、主题内容（2分） 1、内容（1分）：题材不限，内容健康向上；充实生动，有真情实意 2、主题（1分）：寓意深刻，富有感召力 （二）、普通话（3分） 1、发音（1分）：语音准确1分，较准确0.8分，基本准确0.5分，不准确不得分。 2、语速（1分）：语速恰当、声音洪亮，表达自然流畅1分，因不熟练，每停顿一次扣0.1分。 青年教师基本功大赛即兴演讲题目【题目1】我的兴趣爱好【题目2】谈谈内心和谐【题目3】人最难超越的高度就是自己【题目4】我的价值观【题目5】谈谈与人相处【题目6】坚守心灵的一方沃土【题目7】给快乐找个理由【题目8】年轻 没有什么不可以【题目9】心底无私天地宽【题目10】人是需要一点精神的【题目11】我们与时代同行【题目12】生活从“心”开始【题目13】让更多的人快乐 【题目14】面对繁杂的教学工作 你如何调整心态 【题目15】和谐、健康、快乐【题目16】我喜爱的书刊【题目17】你如何发展自己的专业弱点【题目18】善待自己 呵护希望【题目18】.上公开课对一个教师的成长的作用【题目19】培养积极心态 感悟责任人生【题目24】永不言弃 我心永恒 准备时间 3分钟 【题目25】.你怎样做个身心健康的老师【题目26】你如何看待家长满意工程 【题目27】新课程执行过程中 你碰到最棘手的问题是什么【题目28】课堂教学中 你最关注的是什么【题目29】你希望学校领导关心青年教师哪些方面【题目30】谈谈自己的业余生活【题目31】简评最近的工作情况。【题目32】怎样才能提高教师的凝聚力。【题目33】.谈谈做班主任的心得【题目34】.你怎样定义教师【题目35】简介杨森中学【题目36】.点评一位我校的优秀教师【题目37】.如何看待家长的不理解【题目38】.谈谈卫生与健康【题目39】谈谈我校的环境. 【题目40】谈谈如何管理学生【题目41】谈谈你对职业道德的认识【题目42】我参加校本研修之感想。【题目43】“依法治教 注重服务 着力塑造行业形象” 请你谈谈你的设想【题目44】.如何发挥你校师生之特长 【题目45】.怎样调动老师的工作积极性 【题目46】.谈谈你对校本教研的看法。【题目47】.我是怎样备课的。【题目48】.维持校门口的秩序 我的一点想法。【题目49】如何丰富教师的业余生活 缓解教师的心理压力 【题目50】谈谈你对节日文化的认识【题目51】学校活动很多的情况下 你如何调节自己的心态 【题目52】德育倡导“全面德育 全员德育” 请你谈谈自己的理解。【题目53】如何让家长尊重教师 【题目54】你认为提高教育质量应从哪里抓起【题目55】从哪些方面帮助班主任管理学生篇二：教师即兴演讲题目之63个话题 教师即兴演讲题目之63个话题 来源：思雨教育资源网|教学资源|课件论文|作文作者：无边思雨发表日期：2009-5-30 13:16:19 阅读次数： 910 查看权限：普通文章 1、如何维护班集体荣誉？ 2、如何看待学生时代早恋问题？ 3、成人与成才二者是怎样的关系？结合实例说明自己的观点。 4、不同地域、不同背景、不同习惯的同学之间该如何相处？ 5、怎样面对学习、生活中遇到的挫折？ 6、你最崇拜的人是谁？“名人”还是自己？ 7、你认为我们是否应有感恩之心？感恩于谁？ 8、你希望自己会是怎样一位老师？你会如何教育自己的学生？ 9、“言行、仪表”与个人的发展。 10、如今继续提倡“勤俭、节约”作风是否已过时？ 11、在各种资料、媒体中常讲张扬个性，你认为我们该张扬什么样的个性？ 12、三轮车工人方尚礼自己生活的如乞丐，却将自己蹬车收入的35万多元用来资助失学儿童，当病重时，社会捐助给他治病的钱，也被他捐给了希望工程。你对方尚礼的这种行为有何评述？ 13、电视广告不宜过多 14、保护环境是每个人的责任 The way的用法及其含义（一） 有这样一个句子：In 1770 the room was completed the way she wanted. 1770年，这间琥珀屋按照她的要求完成了。 the way在句中的语法作用是什么？其意义如何？在阅读时，学生经常会碰到一些含有the way 的句子，如：No one knows the way he invented the machine. He did not do the experiment the way his teacher told him.等等。他们对the way 的用法和含义比较模糊。在这几个句子中，the way之后的部分都是定语从句。第一句的意思是，“没人知道他是怎样发明这台机器的。”the way的意思相当于how；第二句的意思是，“他没有按照老师说的那样做实验。”the way 的意思相当于as。在In 1770 the room was completed the way she wanted.这句话中，the way也是as的含义。随着现代英语的发展，the way的用法已越来越普遍了。下面，我们从the way的语法作用和意义等方面做一考查和分析： 一、the way作先行词，后接定语从句 以下3种表达都是正确的。例如：“我喜欢她笑的样子。” 1. the way+ in which +从句 I like the way in which she smiles. 2. the way+ that +从句 I like the way that she smiles. 3. the way + 从句(省略了in which或that) I like the way she smiles. 又如：“火灾如何发生的，有好几种说法。” 1. There were several theories about the way in which the fire started. 2. There were several theories about the way that the fire started. The Black Cat ----Edgar Allan Poe Array FOR the most wild, yet most homely narrative which I am about to pen, I neither expect nor solicit belief. Mad indeed would I be to expect it, in a case where my very senses reject their own evidence. Yet, mad am I not -- and very surely do I not dream. But to-morrow I die, and to-day I would unbur d en my soul. My immediate purpose is to place before the world, plainly, succinctly, and without comment, a series of mere household events. In their consequences, these events have terrified -- have tortured -- have destroyed me. Yet I will not attempt to expound them. To me, they have presented little but Horror -- to many they will seem less terrible than baroques. Hereafter, perhaps, some intellect may be found which will reduce my phantasm to the common-place -- some intellect more calm, more logical, and far less excitable than my own, which will perceive, in the circumstances I detail with awe, nothing more than an ordinary succession of very natural causes and effects. From my infancy I was noted for the docility and humanity of my disposition. My tenderness of heart was even so conspicuous as to make me the jest of my companions. I was especially fond of animals, and was indulged by my parents with a great variety of pets. With these I spent most of my time, and never was so happy as when feeding and caress ing them. This peculiarity of character grew with my growth, and, in my manhood, I derived from it one of my principal sources of pleasure. To those who have cherished an affection for a faithful and sagacious dog, I need hardly be at the trouble of explaining the nature or the intensity of the gratification thus derivable. There is something in the unselfish and self-sacrificing love of a brute, which goes directly to the heart of him who has had frequent occasion to test the paltry friendship and gossamer fidelity of mere Man. I married early, and was happy to find in my wife a disposition not uncongenial with my own. Observing my partiality for domestic pets, she lost no opportunity of procuring those of the most agreeable kind. We had birds, gold-fish, a fine dog, rabbits, a small monkey, and a cat.青年教师基本功大赛演讲稿
外研版英语unit3(基础版)
The way常见用法
教师基本功大赛即兴演讲稿
The way的用法及其含义(二)
(完整版)the的用法
The Black Cat读后感
“the way+从句”结构的意义及用法
The Black Cat 原典阅读
way 用法
青年教师朗诵比赛活动方案
教师基本功即兴演讲需要准备几分钟
The way的用法及其含义(一)
中英-the black cat
相关主题
文本预览