# Tagged Questions

A conformal field theory (CFT) is a quantum field theory that is invariant under conformal transformations. In 2D, the infinite-dimensional algebra of local conformal transformations normally permits exact solution or classification of such theories. Further use for CFT applications to string theory,...

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### On the c-theorem

I have been reading a few papers on CFT and AdS/CFT regarding the c-theorem and I have a few questions regarding c-theorems: a) Why is it that the c-theorem is usually considered for only unitary ...
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### Existence of lagrangians at strong coupling

It is well known that some QFT do not admit a lagrangian formulation (like the $(2,0)$ SCFT in $d=6$). Up to my understanding, all the examples that I know of non lagrangian theories are always ...
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### Simple conceptual question conformal field theory

I come up with this conclusion after reading some books and review articles on conformal field theory (CFT). CFT is a subset of FT such that the action is invariant under conformal transformation ...
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### How can one calculate the central term of the conformal field theory algebra (and show it's really the virasoro algebra)?

So I'm following Szabo's book "An Introduction to String Theory and D-brane Dynamics (2nd ed, 2011); still on the canonical treatment in chapter 3. After doing a mode expansion, we get (up to a ...
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### What's the conserved quantities correspond to the generator of conformal transformation

What's the conserved quantity corresponding to the generator of conformal transformations?
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### Renormalization of worldsheet energy-momentum tensor

At the end of section 2.3, Polchinski (in his volume 1) derives the energy-momentum tensor for free massless scalars on worldsheet. He adds a footnote that "the only possible ambiguity introduced by ...
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### Explicit definition of the energy operator in the Ising model

I've simulated a few 2d Ising models at critical temperature on triangular lattice and I'm now trying to check that the correlation functions are right. I alraedy did it for the spin operator ($\sigma$...
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### 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 ...
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### Symmetries in Wilsonian RG (2)

This question is related to the paper http://arxiv.org/abs/1204.5221 and is a continuation of the previous question Symmetries in Wilsonian RG In the liked paper why do the equalities in equation 2....
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### Anyonic Braiding and Conformal Field Theory

I am looking for resources (both pedagogical and newer research articles) on the connection between topological quantum computation and conformal field theory. In particular, a CFT description of ...
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### 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 ...
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### 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 ...
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### 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 ...
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Which textbook of differerntial geometry will have these formulas about conformal transformation? $$\tilde g_{ij} = e^{2\varphi}g_{ij}$$ $$\tilde \Gamma^k{}_{ij} = \Gamma^k{}_{ij}+ \delta^k_i\... 0answers 209 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, ds^2 ... 0answers 201 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 ... 0answers 62 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 ... 0answers 196 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 ... 0answers 220 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 ... 0answers 132 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 ... 0answers 97 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, ... 0answers 245 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 ... 0answers 102 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 ... 1answer 169 views ### Why is conformal field theory so important? I just started escaping the world of quantum mechanics and looking to study quantum field theory. I heard of AdS/CFT and also heard that CFT is of much importance. Now I do not get why having ... 1answer 693 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 - \...
In this article they call weight $(h,\bar{h})=(1,1)$ fields marginal. Why are these fields called marginal? Why are they to be distinguished.
(skip disclaimer) I have a question in Polchinski's string theory book volume 1 p54, related to the Virasoro algebra. Introducing complex coordinates $$w=\sigma^1 + i \sigma^2$$ z=\exp (-i \...