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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 ...
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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, ...
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Meaning of conformal field theory [closed]

Can anyone summarize what conformal field theory is actually about,i.e. 1) what are its goals? (for example, to study such-and-such fields/functions/maps/etc. to see whether they have such-and such ...
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234 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 $\widetilde{\phi}$, ...
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100 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 $1/N$ ...
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160 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} ...
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85 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 ...
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83 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 ...
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179 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 ...
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2answers
253 views

A calculation problem on Conformal Field Theory

This problem is on Di Francesco's book I. It's exercise 7.1: Calculate the norm of the following vector, where $\lvert h\rangle$ is the state of highest weight. $$L_{-1}^n\lvert h\rangle$$ I have ...
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3answers
198 views

Identify the coefficients of Operator Product Expansion (OPE)

Sorry I have a stupid question in Polchinski's string theory book vol 1, p46. For a holomorphic function $T(z)$ with a general operator $\mathcal{A}$, there is a Laurent expansion $$T(z) A(0,0) \sim ...
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2answers
249 views

Conformal fields on compactified manifolds? An apparent paradox!

I would appreciate it if someone tells me how a cft on a compactified manifold (e.g. by means of periodic boundary conditions) can be meaningful? The global conformal invariance is broken due to the ...
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2answers
217 views

Is there a general relationship between the conformal weight of a field and its (classical) scaling dimension?

A field $\phi(z)$ has the conformal weight $h$, if it transforms under $z\rightarrow z_1(z)$ as $$ \phi(z) = \tilde{\phi}(z_1)\left(\frac{dz_1}{dz}\right)^h $$ The (classical) scaling dimension can ...
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1answer
193 views

Massive excitations in Conformal Quantum Field Theory

Single particle states in quantum field theory appear as discrete components in the spectrum of the Poincare group's action on the state space (i.e. in the decomposition of the Hilbert space of ...
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2answers
194 views

Commutation relations of the generators of the conformal group

My question is from P.98 of the book by Di Francesco on Conformal Field theory. He gives the six non-vanishing commutation relations between the elements $P_{\mu}, D, L_{\mu \nu}$ and $K_{\mu}$ ...
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1answer
353 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 ...
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1answer
241 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 ...
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1answer
321 views

What is on the AdS side in AdS/CFT supergravity or string theory?

What really is on the AdS side in AdS/CFT, does it always have to be string theory or is sometimes supergravity "enough" or better suited to do calculations? From the answers to my earlier question, ...
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2answers
389 views

Witten Index and letter partition function

I haven't seen any reference which explains these things and I am not sure of all the steps of the argument or the equations. I am trying to reproduce here a sequence of arguments that I have mostly ...
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1answer
134 views

Why is string theory a two dimensional quantum (conformal) field theory on its worldsheet?

In string theory, we quantize the two dimensional field theory on the string's worldsheet. I have a question about this kind of quantization of string theory: did we have similar theory for point-like ...
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1answer
120 views

Why should a holomorphic function be expanded in Laurent series rather than Taylor series?

In 2d free conformal field theory, there is an operator equation: $$ \partial\bar\partial\hat{X}^\mu\left(z,\bar z\right)=0 $$ Why can it have Laurent expansion like this below rather than Taylor ...
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1answer
167 views

Decomposition of representations of the Virasoro algebra under $sl(2)$

The Virasoro algebra has a finite $sl(2)$ sub-algebra generated by $L_{-1}$, $L_0$ and $L_{+1}$. Let's consider a unitary highest weight representation of the Virasoro algebra with conformal weight ...
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1answer
309 views

Wick Order and Radial Ordering in CFT

I am not so much familiar with the computations tools of conformal field theory, and I just run into an exercise asking to demonstrate the following formula (related to the bosonic field case): ...
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1answer
191 views

Argument for quantum theoretic conformality of $\cal{N}=2$ super-Chern-Simon's theory in $2+1$ dimensions

I am using the standard symbols of $V_\mu$ for the gauge field, $\lambda$ for its fermionic superpartner and $F$ and $D$ be scalar fields which make the whole thing a $\cal{N}=2$ vector/gauge ...
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564 views

Superconformal algebra

I had earlier also asked a question about super conformal theories and I am continuing with that, now with more specific examples. I am quite puzzled with it given that I see no book explaining even ...
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1answer
118 views

Conceptual question about field transformation

(c.f Conformal Field Theory by Di Francesco et al, p39) From another source, I understand the mathematical derivation that leads to eqn (2.126) in Di Francesco et al, however conceptually I do not ...
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1answer
425 views

Classical theories and AdS/CFT

When I was editing the Physics.SE tag wiki for ads-cft, I initially wrote something on the lines of : The AdS/CFT correspondence is a special case of the holographic principle. It states that ...
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1answer
142 views

Name of fermionic CFT theory

I'm looking for a name or references to theories that include a stress energy tensor of the form $$T(z)=A:\phi^\alpha\partial\phi_\alpha:(z)+B:\prod_{i=1}^{D}\phi^i:(z)$$ $\alpha=1,...,D$. Where ...
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votes
1answer
77 views

How can we have massive states of strings and CFT on the string worldsheet at the same time?

Ok, so we can have conformal invariance on a string world sheet. However, it is well known that to preserve conformal symmetry we require states to be massless. So how is it that string theories ...
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2answers
121 views

Path integral derivation of the state-operator correspondence in a CFT

Below, I paraphrase the path integral derivation of the state-operator correspondence in David Tong's notes on CFT (see pdf here). This is my interpretation of the text in that pdf, so please correct ...
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1answer
173 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 ...
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1answer
129 views

A question about vertex operator

(skip disclaimer) I have a question about writing raising and lowering operators in the Schroedinger basis in the section of vertex operator in Polchinski's string theory vol 1 p.68. It is given ...
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1answer
162 views

Time-ordered Derivative and Equal-time Commutator

In Green, Schwarz & Witten Superstring theory, Vol. I, page 141, I don't understand how pulling the derivative inside the Time-ordered product can give an Equal-time Commutator: $$\tag{3.2.44} ...
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1answer
137 views

Virasoro TT OPE in Polchinski's book

I'm trying to understand eq. 2.2.11 in Polchinski's first book. He's computing $$:\partial X^\mu(z)\partial X_\mu(z): :\partial' X^\nu(z')\partial' X_\nu(z'):$$ Now, I understand why this ...
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3answers
551 views

Special conformal transformations and locality

In the conformal symmetry, used in some QFT theories, the infinitesimal generators, applying to space-time, are all linear (translations, rotations, boosts, dilatation), except the special conformal ...
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1answer
263 views

String matrix models with c>1

Question 1: What is the status of string random matrix models (~ triangulated random surfaces) with c>1? In my limited search, I have just come across a few papers by Frank Ferrari (in 2000-2002) on ...
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1answer
135 views

Wick's theorem for calculating OPE

I am trying to understand a calculation using Wick's theorem. Let $T(z)$ be the analytic part of a stress-energy tensor, and $\phi(z)$ a free boson field. Now, ...
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1answer
233 views

QM with complex eigenvalues

What class of theories/physical systems own finite/infinite complex eigenvalues? I do know that e.g., quasinormal modes of BH do have complex eigenvalues, but are they finite or infinite in number? ...
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72 views

(Euclideanized) QFT on $S^d$ vs $S^{d-1}\times S^1$

Broadly I would like to understand what is the difference in the physical interpretation of a (Euclideanized) QFT which is on space-time $S^d$ and which is on a space-time $S^{d-1}\times S^1$. In ...
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153 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) ...
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94 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 ...
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0answers
160 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 ...
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votes
2answers
78 views

Relation between conformal and topological field theories

The Chern-Simons (CS) theory is a topological quantum field theory (TQFT). The question is, is a conformal field theory (CFT) a topological quantum theory? Or the reverse, topological quantum field ...
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1answer
1k views

Why/How is this Wick's theorem?

Let $\phi$ be a scalar field and then I see the following expression for the square of the normal ordered version of $\phi^2(x)$. $$T(:\phi^2(x)::\phi^2(0):) ~=~ 2<0|T(\phi(x)\phi(0))|0>^2 $$ ...
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1answer
124 views

Even-branes in IIA and odd-branes in IIB

The R-R sector of IIA and IIB are respectively given as, $8_s \otimes 8_c = [1]\oplus [3] = 8_v \oplus 56_t$ $8_s \otimes 8_s = [0]\oplus [2] \oplus [4]_+ = 1 \oplus 28 \oplus 35_+$ Now looking at ...
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345 views

How are functional determinants of Laplace-type operators used in physics?

Many mathematical papers concerning the $\zeta$-regularized Determinant of Laplace-type operators refer for motivation to the broad use of such determinants in mathematical physics, especially in ...
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1answer
134 views

Anyons: Effect of braiding on fusion multiplicities

In the theory of non-abelian anyons, essential information is stored in the fusion multiplicities or Verlinde coefficients $N_{ab}^c$. Having the Pants Decomposition in mind, it is possible to use ...
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1answer
294 views

Some questions about the free Fermionic partition function on a circle (Ginsparg's CFT lectures)

The following questions are based on these lectures, http://arxiv.org/abs/hep-th/9108028 I would like to know what is the relationship between the last equation on page 82 ($(L_0)_{cyl} = L_0 - ...
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1answer
240 views

What are the conserved charges related to the Virasoro generators?

I have just learned from reconsidering my demystified book, that when conformally maping the worldsheet of a closed string to the complex plain by using the transformation $z = e^{\tau + i\sigma}$ ...
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1answer
229 views

Conformal Quantum Mechanics

I heard the term Conformal Quantum Mechanics used today. What exactly does this mean? Why would one want to study this?