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Physics

Questions tagged [conformal-field-theory]

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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, statistical mechanics, and condensed matter physics.

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1answer
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In a QFT with Euclidean signature, the correlation functions can only be well-defined in a time-ordered manner (This is Claim 1 on Page 2 of Simmons-Duffin's lecture note). For example, a scalar 2pt ...
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Conformal boundary is defined as the non-degenerate hypersurface where the Weyl factor $\Omega(x)$ vanishes and by non-degeneracy I mean $d \Omega(x)=0$ which is required so that we can determine ...
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In Polchinski's book, it states that the corresponding operators of $|1\rangle, |-1\rangle$ are $\delta(\beta),\delta(\gamma)$, and suggests that it can be shown by path integral. I'm a little ...
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I'm currently reading a lecture note on 2d conformal field theory (2d CFT) by B.Estienne and Y.Ikhlef (EY). It gives an excellent introduction to conformal Ward identities using the Euclidean path ...
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In higher-spin CFT, operators organize themselves into additive multi-twist. I am a bit confused as to the use of "twist-two", "leading-twist", etc. Especially when it mentioned in ...
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Calculations are carried out in Euclidean plane with complexified coordinates $z,\bar{z}$ as we do in CFT. I need to derive the following:$$\int{\frac{d^2 z_1}{(z-z_1)(\bar{z_1}-\bar{w})}}=\pi\ln{|z-...
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Consider a chiral quasi-primary field in 2D with conformal dimension $h$. Under conformal transformation it transforms as:$$\phi^{'}(z)=(\frac{df}{dz})^{h}\phi(f(z)).$$For the two point function of ...
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I am reading this paper by Jiang about $T\bar{T}$ deformations and I came across the following relations$$\mathcal{E}_{n}(R,t)=-R\langle n|T_{yy}^{(t)}|n\rangle\hspace{0.7cm}\mathcal{P}_{n}(R,t)=-i R\...
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Firstly recall the following fact: let $\phi_a,\,a=1,\dots,n$ be the chiral primary fields of a RCFT with respect to the Virasoro symmetry, then we have the following OPE:$$\phi_{a}(z)\phi_{b}(w)=\...
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Why do we say that the (gauge-fixed) worldsheet theory in string theory is a conformal field theory (CFT)? Where exactly does this conformal invariance come from? Is it simply because, after gauge ...
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1answer
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In the path integral of the bosonic string, we fix the gauge by setting the metric $ h $ to a reference metric $ \hat{h} $. A common choice is the conformal gauge:\begin{equation}h_{\alpha \beta} \...
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I am reading Tong's lecture notes on CFT and I can't reproduce a result at pag. 82$$T(z):e^{ikX(w)}:=-\frac{\alpha'^{2}k^{2}}{4}\frac{:e^{ikX(w)}:}{(z-w)^{2}}+ik\frac{:∂X(z)e^{ikX(w)}:}{z-w}+...\tag{...
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Hi :) maybe a stupid question, but I keep getting confused about this so I thought I would ask. I am a student and currently working with conformal field theories. One thing I read repeatedly is that ...
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Consider a general Euclidean QFT (or its lattice regularization).Given a list of all correlators of operators in this theory, and given that they are reflection-positive, how can one explicitly ...
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I want to get more comfortable working with conformal field theory so I'm going over the problems of the "Yellow pages" (Conformal Field theory by Di Francesco et al.) and I got stuck in ...

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