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10
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255 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. ...
8
votes
0answers
213 views

Holomorphic Factorization in CFT$_2$

Is a CFT$_2$ always holomorphically factorizable? I had this idea because that's what we usually see is taken in string theory e.g (taking $z$ and $\bar{z}$ as independent variables). E.g. Ginsparg ...
7
votes
0answers
259 views

Dimensional regularization and IR divergences and scale invariance

I want to know if dimensional regularization has any issues if the theory has IR divergences or is scale invariant. Does dimensional regularization see "all" kinds of divergences? I mean - what ...
6
votes
0answers
167 views

2d Ising model in CFT and statistical mechanics

When I recently started to read about conformal field theory, one of the basic examples there is the so called Ising model. It is characterized by certain specific collection of fields on the plane ...
6
votes
0answers
103 views

d=2 O(3) sigma model becomes “conformal antiferromagnet”

In Advanced topic in quantum field theory / M. Shifman on page 251 the author discusses the fact that the theta term is topological and does not affect the equations of motion. Then he said: "In ...
6
votes
0answers
392 views

Trace of stress tensor vanishes ==> Weyl invariant

You often see in textbooks the statement that ${T^\mu}_\mu = 0$ implies Weyl invariance or conformal invariance. The proof goes like $\delta S \sim \int \sqrt{g} T^{\mu\nu} \delta g_{\mu\nu} \sim ...
6
votes
0answers
181 views

Toda equations and surface operator

I would like to know the reason why the equation (14) in the paper by Yamada is called the Toda equation. \begin{equation} \left[\frac12\sum_{i=1}^N\left(y_i\frac{\partial}{\partial ...
5
votes
0answers
167 views

Do “typical” QFT's lack a lagrangian description?

Sometimes as a result of learning new things you realize that you are incredibly confused about something you thought you understood very well, and that perhaps your intuition needs to be revised. ...
5
votes
0answers
166 views

Zamolodchikov's c-theorem paper

I am reading the 1986 paper [1] where Zamolodchikov proves the c-theorem and I would like to understand how equations (7a), (7b) and (8) are derived from the Callan-Symanzik equation. For ...
5
votes
0answers
81 views

BTZ Black Hole Central Charge and Conformal Weight

I have been trying to reproduce a calculation (equation 4.12) in this paper http://arxiv.org/pdf/1107.2678v1.pdf by Carlip reviewing the derivation of the effective central charge of the BTZ Black ...
5
votes
0answers
34 views

When does the correlator of a string of fields and the current vanish “sufficiently fast” at infinity and Ward's identity?

One consequence of the Ward identity (cf. Di Francesco et al) is that it means variation of correlators under infinitesimal transformation is zero. This can be seen by integrating the ward identity, ...
5
votes
0answers
330 views

What is the connection between Conformal Field Theory and Renormalization group in QFT?

As I know, the fundamental concept of QFT is Renormalization Group and RG flow. It is defined by making 2 steps: We introduce cutting-off and then integrating over "fast" fields $\widetilde{\phi}$, ...
5
votes
0answers
103 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
0answers
184 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} ...
5
votes
0answers
89 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 ...
5
votes
0answers
84 views

Defects in 3+1 TFTs/2+1 CFTs

I would like to know of good pedagogic references to learn about the notion of "defects" in TFTs and CFTs. I am specially interested in 3+1 TFTs (.and probably about their relation to 2+1 CFTs..) In ...
5
votes
0answers
184 views

Is string theory over a time varying background a conformal field theory to all orders in perturbation theory?

When computing the first order perturbative corrections to string theory over a curved background, we find the background has to be Ricci-flat if the dilaton is constant and we have no fluxes. Such is ...
4
votes
0answers
60 views

Why the bosonic part of the superconformal group $SU(2,2|1)$ is $SO(4,1) \times U(1)_R$?

Why in $d=4$ $\mathcal{N}=1$ SCFT the bosonic part of the superconformal group $SU(2,2|1)$ is $SO(4,1) \times U(1)_R$? More generally how can I determine the such a thing in other theories? Is there ...
4
votes
0answers
168 views

Expressions of action and energy momentum tensor in bc conformal field with central charge equals one

I have a question with conformal field theory in Polchinski's string theory vol 1 p. 51. For $bc$ conformal field theory $$ S=\frac{1}{2\pi} \int d^2 z b \bar{\partial} c $$ $$ T(z)= :(\partial b) ...
4
votes
0answers
106 views

Identity in CFT

I heard and read couple of times reference to a certain identity in conformal field theory (maybe specific to two dimensions). The identity relates the trace of stress-energy tensor to the beta ...
4
votes
0answers
166 views

Wilson lines, boundary conditions, surface defects of TQFTs

I asked the following question in mathematics stack exchange but I'd like to have answers from physicists too; I have been studying (extended) topological quantum field theories (in short TQFTs) from ...
3
votes
0answers
51 views

Are the following terms, related to scale invariance and renormalization in QFT, equivalent?

Which of the following terms are equivalent? and in what cases/limits do the non-equivalent terms become equivalent? A) a scale invariant quantum field theory. B) a conformal quantum field theory. ...
3
votes
0answers
46 views

Conserved charge of a conformal transformation

From Becker, Becker and Schwarz String Theory and M-Theory: For the infinitesimal conformal transformation $$\tag{3.25}\delta z=\varepsilon(z)\quad\text{and}\quad \delta\bar ...
3
votes
0answers
85 views

Non-abelian bosonization

Reading this review about non-abelian bosonization, Non-abelian bosonization by I.Karmazin, I stumbled about two questions Below equation 6, I don't get the final point in the statement about the ...
3
votes
0answers
111 views

Question about derivation of tensor in Di Francesco's CFT

This is a question for anyone who is familiar with Di Francesco's book on Conformal Field theory. In particular, on P.108 when he is deriving the general form of the 2-point Schwinger function in two ...
3
votes
0answers
120 views

Derivation of the Noether current

(c.f Di Francesco et al, Conformal Field Theory, pp40-41) I am trying to derive eqn (2.142) or $\delta S = \int d^d x \partial_{\mu}j^{\mu}_a \omega_a$ in the book CFT by Di Francesco et al. I have ...
3
votes
0answers
118 views

Virasoro Operators commutation relations

For the commutation relation in quantising the bosonic string $\left[L_n,L_{m}\right]=(n-m)L_{n+m}+\frac{D}{12}n(n^2-1)\delta_{n+m,0}$ we can then calculate this for $m=-n$ in between the vacuum ...
3
votes
0answers
131 views

Questions on entanglement entropy

If the spatial entangling surface is $M$ then it seems that one way to get the entanglement entropy is to think of the QFT on the manifold $S \times M$ where $S$ is a 2-manifold with the metric, ...
3
votes
0answers
148 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 ...
3
votes
0answers
58 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
90 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 ...
3
votes
0answers
423 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 ...
3
votes
0answers
160 views

Questions about classical and quantum scale invariance

This is kind of a continuation of this and this previous questions. Say one has a free "classical" field theory which is scale invariant and one develops a perturbative classical solution for an ...
3
votes
0answers
175 views

Conformal symmetry of Navier-Stokes?

This question is in reference to the paper arXiv:0810.1545 Can someone help understand this scaling argument and the proof(?) that there is a conformal symmetry in Navier-Stoke's equation? (..am I ...
3
votes
0answers
127 views

Derivation of the enhancement of U(1)$_L$ x U(1)$_R$ to SU(2)$_L$ x SU(2)$_R$ at the self-dual radius

Towards the end of the paragraph with the title String theory's added value 2: enhanced non-Abelian symmetries at self-dual radii and abstract C with current algebras of this article, it is explained ...
3
votes
0answers
89 views

Relating the deformation of Calabi-Yau metrics and the conformal quantum field theories

(v2) As I read e.g. in this question, the nice holonomy group features of Calabi-Yau manifolds are valuable regarding supersymmetry (I suspect because it's a symmetry involving the target manifold, ...
3
votes
0answers
209 views

Central charge at the fixed point of the ${\cal N}=2$ Landau-Ginzburg theory in $1+1$ dimensions

Let me first believe that the ${\cal N}=2$ Landau-Ginzburg theory does in the IR flow to a non-trivial fixed point and that if the potential is of the form $\Phi ^k$ then the central charge of the CFT ...
3
votes
0answers
92 views

How to construct a 2D conformal field on a mirrored annulus with a looping pattern?

I would like to construct a 2D conformal field on an annulus in which the inner and outer boundaries are like mirrors, and can be approximated by regular polygons (with the same number n of mirror ...
2
votes
0answers
24 views

Vertex operator and normal ordering

The two point function, or propagator for a free massless boson, $\phi$ in 2 dimensions is given by, $\begin{equation} \langle \phi (z,\bar{z})\phi(\omega, \bar{\omega})\rangle = ...
2
votes
0answers
24 views

Is there a Ramond vacuum for real fermions?

When studying the CFT of a complex fermion $\Psi$ we know that if it's periodic, ie if $$\Psi(\sigma_1+2\pi,\sigma_2)=\Psi(\sigma_1,\sigma_2)$$ then there is a doubly degenerate Ramond vacuum which I ...
2
votes
0answers
50 views

Questions about the existence of 5d & 6d version of 4d ${\cal N}=2$ SCFTs

Given a 4d N=2 Superconfomal field theory (SCFT) with a global flavor symmetry ( $\mathfrak{f}$ as the corresponding lie algebra), can we clam that this theory can always flow from a 5d ${\cal N}=1$ ...
2
votes
0answers
37 views

Monodromy, Holonomy and Braiding Phase

In quantum Hall effect, especially in the context of CFT description, these words come up often. I think I understand the braiding phase - as the phase gained by the wave function when a quasi ...
2
votes
0answers
77 views

Stack presentations and massive non-conformal theories

In the paper, Cluster Decomposition, T-duality, and Gerby CFT’s , by Hellerman, Henriques, Pantev and Sharpe, in the introduction it says: "Briefly, the idea is that nearly every stack has a ...
2
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0answers
41 views

CFT calculation of the Partitionfunction of $2+1$ dimensional gravity

I want to reproduce formula (4.29) in http://arxiv.org/abs/0804.1773v1 given by: $$ Z=Tr(q^{L_{0}}\bar q^{\bar L_{0}})=|q|^{-2k} \prod^{\infty}_{n=2}\frac{1}{|1-q^{n}|^{2}} $$ Where the trace is ...
2
votes
0answers
40 views

Non translation invariant correlator in CFT

I'm doing an exercise on vertex operators in the CFT book by Di Francesco & al.; exercise 9.2 p.329 : Using mode expansion show that: $$\langle\tilde{\phi(z)}\tilde{\phi(w)}\rangle= - \text{ln} ...
2
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0answers
54 views

Possible Error in deriving conformal generator

My professor gave me the following derivation for the full generator of the Lorentz transformations. The starting point is to consider a subgroup of the conformal group that leaves the origin fixed ...
2
votes
0answers
61 views

Anomalies from a Renormaization Group Equation (RGE)

This is an approach to anomalies which seems unfamiliar to me.. Firstly what is this function $W$ which seems to satisfy the equation, $\frac{\partial W }{\partial g^{\mu \nu} } = \langle T_{\mu ...
2
votes
0answers
51 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 ...
2
votes
0answers
94 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 ...
2
votes
0answers
103 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 ...