# Questions tagged [conformal-field-theory]

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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### How to derive Kac-Moody and Virasoro algebras from their descriptions as central extensions?

I am following the notes (https://arxiv.org/abs/hep-th/9904145) to learn conformal field theory, and want to know how to derive the contributions to the Virasoro and Kac-Moody algebras from the ...
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### Conformal weight of a coset model, and a specific case

Given a coset model $(G\times SO(2d))/H$, what is the expression for its conformal weight (in terms of its central charge or, alternatively, in terms of the highest weights of irreducible ...
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### Simple calculation on coordinate transformation of Lagrangian (Qaulls' CFT lecture note)

I have a question while reading "Lectures on conformal field theory" by Qaulls (https://arxiv.org/abs/1511.04074). $^1$ Question. I cannot find that the transformation (1.12) makes the action ...
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### Weight $h$ as a function of the central charge $c$ in a Unitary Highest Weight Irrep of the Virasoro algebra

A highest weight irreducible representation of the Virasoro algebra can be labelled uniquely by $(c,h)$, with $c$ the central charge and $h$ the "Witt weight" (the weight of the Witt algebra part of ...
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### Is there a way to make this simple “derivation” of the Trace Anomaly correct?

I think I came up with a simple yet sketchy almost-proof of the trace anomaly (A.K.A. Weyl anomaly) in 2D CFT, but it has the wrong prefactor. I was wondering if anyone could assess whether this "...
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### Conformal Invariance of Maxwell's Equations

I am currently doing some conformal field theory (in four dimensions) and want to show the invariance of Maxwell's equations under conformal transformations, in particular \begin{align} \partial_\...
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### Field strength renormalization and the energy-momentum tensor

This question is about the connection between the energy-momentum tensor, dilation transformations, and field renormalization. From a Wilsonian perspective on renormalization we start out with a ...
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### How to properly make sense of the $\mathcal{S}$-matrix as a correlator on a sphere?

In the book "Lectures on the Infrared Structure of Gravity and Gauge Theories" by Andrew Strominger, the author discusses in Chapter 3 the idea of "The $\mathcal{S}$-matrix as a Celestial Correlator". ...
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### Weyl transformation of Ricci tensor

We define the Weyl transform as, $$\tilde{g}_{\mu\nu}=\Omega^2g_{\mu\nu},$$ wherein $\Omega^2$ is a scalar function of space-time $x$. The Weyl transformed Christoffel symbol can be obtained by ...
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### Importance of an extra total derivative term in Liouville theory

In this paper on boundary Liouville theory, the authors have introduced an extra term, $-\partial_{\sigma}^2\phi$, (the last term in the equation below) in defining the stress tensor of the Liouville ...