# 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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### Radial quantization and infrared divergences

I am reading Ginspard lectures "Applied CFT" http://arxiv.org/abs/hep-th/9108028 which is not my first material on the subject. He tries to motivates radial quantization on the reason that ...
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### What is the physical interpretation of the S-matrix in QFT?

A few closely related questions regarding the physical interpretation of the S-matrix in QFT: I am interested in both heuristic and mathematically precise answers. Given a quantum field theory when ...
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### Question on Section 9.1.3 in “Conformal Field Theory” by Philippe Di Francesco et. al

Question on Section 9.1.3 in "Conformal Field Theory" by Philippe Di Francesco et. al. The basic idea of the Coulomb-gas formalism is to place a background charge in the system, making the $U(1)$ ...
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The edge of a fractional quantum Hall state is a chiral conformal field theory. In the Laughlin case it corresponds to the chiral boson, S = \frac{1}{4\pi} \int dt dx \left[\partial_t\phi\... 0answers 185 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 ... 1answer 273 views ### constraint on scaling dimension How can we show that for any scalar operator \Delta\geq1 (where \Delta is the scaling dimension)? Where can I find a reference for reading where it comes from? 1answer 202 views ### Definition of CFT A standard QFT cannot be defined as a set of Poincare-invariant correlation functions because this does not take into account the possibility of non-perturbative effects (e.g. instantons) Can we ... 2answers 672 views ### Invariance of Maxwell's Equations under inverting variables - Reference and use Some months ago, an ArXiv paper mentioned in passing that Maxwell's Equations were invariant under reciprocating the variables, or at least this results in a dual set of Maxwell Equations. (Actually I ... 1answer 646 views ### Clarification on “central charge equals number of degrees of freedom” It's often stated that the central charge c of a CFT counts the degrees of freedom: it adds up when stacking different fields, decreases as you integrate out UV dof from one fixed point to another, ... 0answers 470 views ### Breaking of conformal symmetry I am wondering something about the breaking of conformal symmetry: I know that it can be broken at the quantum level, anomalously, but I never encountered or heard about a model where it is broken "à ... 2answers 477 views ### 2D Ghost CFT and two-point functions For some reason I am suddenly confused over something which should be quit elementary. In two-dimensional CFT's the two-point functions of quasi-primary fields are fixed by global SL(2,\mathbb C)/\... 5answers 4k views ### Conformal transformation/ Weyl scaling are they two different things? Confused! I see that the weyl transformation is g_{ab} \to \Omega(x)g_{ab} under which Ricci scalar is not invariant. I am a bit puzzled when conformal transformation is defined as those coordinate ... 1answer 92 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 ... 1answer 226 views ### Conformal Invariance and the OPE I am reading Polchinski's String Theory now and am having trouble with a couple of things mentioned on Page 45 under "Conformal Invariance and the OPE". Here is the paragraph I am reading. The ... 1answer 523 views ### Equivalent definitions of primary fields in CFT I have come across two similar definitions of primary fields in conformal field theory. Depending on what I am doing each definition has its own usefulness. I expect both definitions to be compatible ... 0answers 196 views ### 't Hooft's landscape of conformally constrained QFTs As described in "A class of elementary particle models without any adjustable real parameters", "The Conformal Constraint in Canonical Quantum Gravity", and "Probing the small distance structure of ... 1answer 164 views ### Constraining two-point functions of boundary operators on the disk I'm trying to understand the constraints on the disk CFT correlation function \langle O_1(y_1)O_2(y_2)\rangle, where the O_i's are boundary operators that are not necessarily primary. It's a well-... 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 ... 1answer 193 views ### Exercise QFT and CFT Consider the action functional S[z;t_1,t_2]=\int_{t_1}^{t^2}[g(z,\bar{z})\dot{z}\dot{\bar{z}}]^{\frac{1}{2}}dt with z(t) a complex path with end points z_i=z(t_i),\; i=1,2. g(z,\bar{z}) is a ... 1answer 255 views ### 1-Dimensional Sigma Models I'm currently interested in 1-dimensional (linear) Sigma Models. In the theory of 2-Dimensional GLSM, the fields can be viewed as an embedding of the worldsheet in some target Manifold of higher ... 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, ... 1answer 192 views ### The neutrality condition and the (non)-vanishing of the one-point correlator for the bosonic vertex operator Consider the massless scalar field Hamiltonian, \begin{align} H = \frac{1}{2}\int \Pi^2- (\partial_x\phi)^2 dx \end{align} with \Pi \sim \partial_t\phi the conjugate field of \phi. This ... 2answers 314 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 ... 0answers 100 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 ... 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 ... 2answers 561 views ### A certain regularization and renormalization scheme In a certain lecture of Witten's about some QFT in 1+1 dimensions, I came across these two statements of regularization and renormalization, which I could not prove, (1) \int ^\Lambda \frac{d^2 k}... 0answers 192 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. \left[\frac12\sum_{i=1}^N\left(y_i\frac{\partial}{\partial y_i}-y_{i+1}\frac{\... 1answer 243 views ### A certain \cal{N}=2 superconformal theory (or is it?) I want to look at the following theory in 1+1 dimensions with \Phi being the chiral superfield, L = \int d^2x d^4\theta \bar{\Phi}\Phi - \int d^2x d^2\theta \frac{\Phi^{k+2}}{k+2} - \int d^2x d^... 2answers 618 views ### Branch-point twist fields and operator insertions on a Riemann manifold I am having trouble understanding how Eq (2.6) in this paper (PDF)Z[\mathcal{L},\mathcal{M}_{n}]\propto\langle\Phi(u,0)\tilde{\Phi}(v,0)\rangle_{\mathcal{L}^{(n)},\mathbb{R}^{2}} generalizes to ...
Let the free electromagnetic current $J_\mu(x)$ be = $:\bar{\psi}(x)\gamma_\mu Q \psi(x):$ where $::$ is the normal ordering. In this expression why is $Q$ thought of as a "charge operator" instead ...