The tag has no wiki summary.

learn more… | top users | synonyms (1)

2
votes
0answers
47 views

stress tensor in Kazama-Suzuki construction

This is a technical question about equation (2.42) of the original paper [KS] of the Kazama-Suzuki construction. I think the authors did a simple substitution ...
1
vote
1answer
101 views

Large-N factorization of single-trace operators

Does anyone know where I can find a pedagogical explanation of large-N factorization in SU(N) gauge theories or nonlinear O(N) sigma models (in the latter case the trace corresponds to a dot product). ...
2
votes
0answers
85 views

Regulating an infinite sum in the $bc$ CFT

The EM tensor of the $bc$-CFT is $$ T(z) = \colon \partial b c \colon - \lambda \partial \colon b c \colon $$ After expanding in a mode expansion, we find $$ T(z) = \sum_{m} \frac{1}{z^{m+2}} \sum_n ...
7
votes
1answer
347 views

Is Conformal Symmetry Local or Global?

I'm just brushing up on a bit of CFT, and I'm trying to understand whether conformal symmetry is local or global in the physics sense. Obviously when the metric is viewed as dynamical then the ...
1
vote
0answers
109 views

Why Liouville theory is interesting? [closed]

What makes Liouville theory subject to relatively intense research field?
1
vote
0answers
78 views

Central charges c and topological ground state degeneracy GSD

A 2+1D topological field theory (topologically ordered states), implies that the topological ground state degeneracy (GSD) on $T^2$ torus (2D manifold without boundary). For example a level k U(1) ...
16
votes
2answers
473 views

S-Matrix in $\mathcal{N}=4$ Super-Yang Mills

This is a general question, but what is meant when people refer to the S-Matrix of $\mathcal{N}=4$ Super Yang Mills? The way I understood it is the S-Matrix is only well defined for theories with a ...
10
votes
0answers
184 views

Orbifold CFT of SU(2)/G and SO(3)/G

In this paper by Dijkgraaf, Vafa, Verlinde, Verlinde, orbifold CFT is discussed. In that paper, it outlined that orbifold CFT provides a way to generate the new theories from the old known ones. ...
2
votes
0answers
82 views

Half-integer Spin and “natural conformal dimension”

If we consider a classical field theory for a massless particle of integer spin $s$, in a curved space-time, one finds that it is "naturally" conformal in a space-time of dimension $2+2s$ For ...
2
votes
1answer
161 views

Stress-energy Trace of Massless Klein Gordon Field

I've calculated the trace of the stress-energy for a massless KG field and I keep getting $T = - (\partial \phi)^2$ in 3+1 dimensions. I'm using $$T_{\mu\nu} = \partial_\mu \phi \partial_\nu \phi - ...
1
vote
0answers
65 views

Action of conformal generators on fields

I am calculating the action of the conformal generators on fields, to be more precise on wavefunctions. For now, I'm classical. I will just paste the part of my report on this to show what I am ...
2
votes
1answer
96 views

Transferring CFT correlations from $\mathbb{R}^3$ to $S^3$

There seems to be a simple method to transfer a CFT's correlations from $\mathbb{R}^3$ to $S^3$ but I am not understanding why it is supposed to work. The idea is that somehow because, $ds^2_{S^3} = ...
3
votes
1answer
234 views

A key relation in Di Francesco's book on Conformal Field Theory

Recently I am reading Di Francesco's book Volume I on Conformal Field Theory. In order to reduce the number of fields in a correlator, the calculation of Operator Algebra is extremely important. To do ...
3
votes
0answers
93 views

Moduli Space of $\mathcal{N}=4$ SYM on $\mathbb{R} \times S^3$

When we define $\mathcal{N}=4$ SYM on flat Minkowski space, the supersymmetric vacua are parametrized by scalars living in the cartan subalgebra of the gauge group. A generic point in the moduli space ...
10
votes
1answer
435 views

Operator-state correspondence in QFT

The operator-state correspondence in CFT gives a 1-1 mapping between operators $\phi(z,\bar{z})$ and states $|\phi\rangle$, $$ |\phi\rangle=\lim_{z,\bar{z}\mapsto 0} \phi(z,\bar{z}) |0\rangle $$ where ...
5
votes
3answers
212 views

Error in books of conformal field theory?

If you look at the book Conformal Field Theory (by Philippe Francesco, Pierre Mathieu and David Senechal) or the lecture notes Applied Conformal Field Theory (by Paul Ginsparg), and many other places: ...
0
votes
1answer
145 views

Modular invariance of CFT

I am looking at the Cardy formula for entropy in CFT, and in the article 'Kerr/CFT correspondence and its Extensions' there is a sentence: In any unitary and modular invariant CFT, the asymptotic ...
4
votes
1answer
138 views

Hermitian conjugation in Radial Quantization

I'm a little confused about Hermitian conjugation in a radially quantized CFT. Now, in the Minkowski theory, Hermitian conjugation leaves the coordinates invariant, i.e. $t^\dagger = t$ and $x^\dagger ...
5
votes
2answers
102 views

Do primary fields (in a CFT) satisfy the wave equation?

In a 2-dimensional CFT, do primary fields generally satisfy the wave equation? I know that if they have either purely holomorphic or purely anti-holomorphic, they do. But what about a general primary ...
0
votes
0answers
50 views

Why isn't the 3 pts function vanishing in the Ising model by Z_2 symmetry?

The Ising model with vanishing external field possesses the $Z_2$ symmetry: $$\sigma_i \rightarrow - \sigma_i$$ implying that the 1 pt function vanishes: $$<\sigma_i> \;= 0$$ In the same ...
3
votes
0answers
52 views

Free energy of the critical U(N) model

Can someone help explain how the equations 30, 31 and 34 were obtained in this paper. At a conceptual level I am wondering looking at equation 34 as to if they mean that $\lambda$ is somehow the ...
3
votes
0answers
76 views

Link between anomalous dimensions and fractal dimensions

I just realized that anomalous dimensions in quantum/statistical field theory is not that different from fractal dimensions of objects. They both describe how quantitaive objects transform under a ...
2
votes
1answer
82 views

Steepest descent for Mellin-type integration

Here I would like to see the behavior of a function as an integral when its argument (which is a parameter in the integral) goes to zero. If I try to evaluate an integral $$I(\lambda) = ...
6
votes
2answers
170 views

How does a SCFT avoid the Haag-Lopuszanski-Sohnius theorem?

According to the Haag-Lopuszanski-Sohnius theorem the most general symmetry that a consistent 4 dimensional field theory can enjoy is supersymmery, seen as an extension of Poincarè symmetry, in direct ...
5
votes
0answers
98 views

“Light” states in critical $O(N)$ model in $2+1$ (and holography)

Let me split the question in a few parts, Can someone give me a reference which explains the CFT properties of the critical $O(N)$ model in $2+1$? Like how are the CFT correlators (in a $1/N$ ...
5
votes
1answer
140 views

Why do three dimensional gauge theories flow to conformal theories in the infrared?

What is meant with the fact that Super Yang-Mills flows to a conformal field theory in the infrared? Also, is this a general fact or does this depend on the fact of considering a certain class of ...
1
vote
1answer
60 views

Ghosts on Torus worldsheet

Why after the expansion, only 0-mode of bc-ghost contributes to the 4-points ghost function on a torus worldsheet? $$<c(z_1)b(z_2)\tilde{c}(\bar{z}_3)\tilde{b}(\bar{z}_4)>_{T^2} ...
11
votes
1answer
287 views

What is the CFT dual to pure gravity on AdS$_3$?

Pure $2+1$-dimensional gravity in $AdS_3$ (parametrized as $S= \int d^3 x \frac{1}{16 \pi G} \sqrt{-g} (R+\frac{2}{l^2})$) is a topological field theory closely related to Chern-Simons theory, and at ...
3
votes
0answers
343 views

A gentle introduction to CFT [closed]

Which is the definition of a conformal field theory? Which are the physical prerequisites one would need to start studying conformal field theories? (i.e Does one need to know supersymmetry? Does one ...
5
votes
0answers
129 views

Some questions about calculation central charge in a CFT in $d$ spacetime dimensions

This is based on this paper, http://arxiv.org/abs/hep-th/0212138 For a CFT on a $S^d$ spacetime (of radius R) it seems to be claimed that the central charge is given by, $ c = \langle \int_{S^d_R} ...
0
votes
0answers
52 views

One forms in projective null cone

In the embedding formalism one works in $d+2$-dimensions with coordinates in a $d+1$ suface called projective null cone. Here, linear $SO(d,2)$ transformations on the embedding space induce conformal ...
5
votes
0answers
78 views

RG flow from a UV scale invariant field theory to a gapped phase in the IR

On the section 3 of http://arxiv.org/abs/1309.2921 the authors consider the RG flow from a scale invariant field theory in the UV to a gapped theory in the IR. The theory is couple to a background ...
3
votes
1answer
203 views

Deriving Virasoro algebra question

I'm reading a book Lie groups, Lie algebras, cohomology and some applications in physics by Azcarraga and Izquierdo, and on page 347, when deriving the exact form of the central extension term I came ...
1
vote
1answer
97 views

Lightcone singularity of a 3 point function in CFT

I had a quick question regarding the title of the question. In e.g. 2D CFT (for simplicity), the three point function of three operators with conformal dimension $a$, $b$ and $c$ are given as $$ ...
4
votes
1answer
271 views

Representations of the Conformal Group in terms of the Poincare Group Reps

The Conformal group contains the Poincare group. Typically, if you take a representation of a group and then look at it as a representation of a subgroup, the representation will be reducible. I often ...
12
votes
2answers
354 views

Why are there no particles in conformal theories?

In Matt Strassler's recent post (here) he makes the statement that scale invariant (I assume he means conformally invariant, more generally) theories have no particles in them. What's the reason for ...
6
votes
1answer
287 views

Is integrability necessary for the Amplituhedron?

It is well known that there exist mappings between operators in N = 4 Super Yang–Mills and spin chain states making the theory Bethe Ansatz integrable. Is integrability a necessity for the ...
10
votes
1answer
251 views

Scale invariance plus unitarity implies conformal invariance?

What has the reaction been towards the recent paper claiming to have a proof that scale invariance plus unitarity implies conformal invariance in 4d?
2
votes
1answer
99 views

Conformal dimensions of the energy-momentum tensor

Currently I am reading the Di Francesco-Mathieu-Sénéchal textbook on conformal field theory. Above the equation 5.52, the author argues that the EM tensor should have scaling dimension 2 and spin 2. ...
4
votes
1answer
219 views

Some questions about the paper, “AdS description of induced higher spin gauge theory”

I am referring to this paper. I guess that in this paper one is trying to relate the massless spin $s$ gauge fields in $AdS_4$ to conformal spin $s$ theory on $S^3$. So am I right that the ...
16
votes
1answer
516 views

What does it mean for a QFT to not be well-defined?

It is usually said that QED, for instance, is not a well-defined QFT. It has to be embedded or completed in order to make it consistent. Most of these arguments amount to using the renormalization ...
3
votes
1answer
215 views

Expectation value of the stress-energy tensor in 2-D CFT

Due to a previous question, I am confused with the expectation value of the stress-energy tensor in a 2-D conformal field theory. Let's take the example of string theory, to sketch the problem. ...
6
votes
2answers
185 views

Anomalies and Modification of symmetry algebra

This question is motivated by 2-dimensional CFTs where the Classical conformal group (defined by the Witt algebra) is modified to the Virasoro algebra in the quantum theory. In this question, it was ...
8
votes
2answers
291 views

Central charge in a $d=2$ CFT

I've always been confused by this very VERY basic and important fact about two-dimensional CFTs. I hope I can get a satisfactory explanation here. In a classical CFT, the generators of the conformal ...
3
votes
0answers
238 views

Traceless of stress-energy tensor in $d=2$

This is a question regarding Francesco, section 4.3.3. In this section, he considers the two-point function $$ S_{\mu\nu\rho\sigma}(x) = \left< T_{\mu\nu}(x) T_{\rho\sigma}(0)\right> $$ He then ...
2
votes
2answers
97 views

Factor of two differences for free field Green's functions in conformal field theory

I have a question about the expressions for free field Green's functions in conformal field theory. It comes from three origins 1) In Polchinski's string theory volume I p36, it is given $$ ...
3
votes
1answer
213 views

Massless fields in curved spacetimes

I read the following statement in one of Penrose's paper zero rest-mass field equations can, with suitable interpretations, be regarded as being conformally invariant. I take this to imply that ...
2
votes
1answer
107 views

OPE and 4-point correlation function in CFT_d

I'm reading this paper where to determine the coefficient $C^{\phi\phi O}(x_{12},\partial_2)$ of the OPE (p.10) $$\phi^\alpha (x_1)\phi^\beta (x_2)=C_\phi ...
5
votes
1answer
173 views

The basic equation of bosonization

[..quoting from Page 11 of Polchinski Vol2..] Given $1+1$ conformal bosonic fields $H(z)$ one has their OPE as, $H(z)H(0) \sim -ln(z)$ Then from here how do the following identities come? ...
2
votes
1answer
119 views

representation of conformal group in d>2

In P. Di Francesco, P. Mathieu, D. Snchal they fix the generators of the conformal group acting on a scalar field by somewhat arbitrarily defining $$\Phi'(x)=\Phi(x)-i\omega_a G_a\Phi(x)$$ and by ...