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Questions tagged [conformal-field-theory]

Used for questions related to conformal field theory, which is a quantum field theory that is invariant under conformal transformations.

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Rewriting a state as a field in CFT

I've been working through a textbook and course on conformal field theory recently. However in a section illustrating how to calculate correlators for secondary fields (using the free boson as an ...
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Convergence of scalar product in a hilbert space

Background: From this paper I'm trying to understand why the OPE in conformal field theory has a finite radius of convergence. The authors make the claim that the scalar product of two states ...
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Prove two Integrals formulae in two dimension

I come across the following two integral formulae The first integral formula is \begin{equation} \int_\Bbb C d^2z |z|^{2a}|z-x|^{2c}|z-1|^{2b} = \frac{S(a)S(c)}{S(a+c)}|I_{0x}|^2+\frac{S(b)S(a+b+c)}{...
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Grasping the idea of Virasoro Algebras in 2D Conformal field theory

I have been trying to understand the connection between Virasoro algebras and CFT. After a course in string theory, I was under the impression that the Virasoro algebra was simply the Lie algebra of ...
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How the line element change in a complex change of variables?

So I'm learning conformal field theory and having a hard time to prove the conformal Ward identity. From the lectures notes from John Cardy, he express the integral $$ \delta S = \frac{1}{2\pi} \...
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Understanding Moonshine and Heterotic E8xE8

Recently I have become familiar with the conjectured relationship of monstrous moonshine and pure $(2+1)$-dimensional quantum gravity in AdS with maximally negative cosmological constant and, it’s ...
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Looking for easy materials on Conformal Field Theory for beginners

Question: I'm a math student in senior year. I want to know about CFT(as the title explained). For related knowledge, I've learned basics about Differential Geometry, Differential manifolds. I want to ...
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Two-point function of massless scalar theory in 2d CFT

Following the derivation of the massless free-boson two-point function given in Di Francesco, Mathieu and Sènèchal, I had an apparently stupid doubt. Look at the attached picture. Where does the ...
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Contour Deformation in a Conformal Field Theory

Consider the discussion on page 77 of James Lepowsky and Haisheng Li's Introduction to Vertex Operator Algebras and Their Representations. In particular, the authors state that The operator product ...
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Why is conformal invariance only possible for massless theories?

A usual mantra in field theories is the assertion that only massless theories can be conformally invariant. By a theory I mean an action $$ S = \int \mathcal{L} \, \mathrm{dVol}, $$ where $\mathcal{L}$...
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Reference request: 2D conformal field theory and the honeycomb lattice

Would anyone know what is meant by "conformally invariant" functions defined on the plaquettes of the honeycomb lattice (ie the function is defined on the vertices of the dual tringular lattice)? ...
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CFT's vs Vertex Operator Algebras

I am trying to clear my ideas about the relation between a Conformal Field Theory (CFT) and a Vertex Operator Algebra (VOA). For me a CFT based on a (complex) vector space $H$ is a projective monoidal ...
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Conformal group in two dimensions

In Conformal field theory, physicist says, the conformal group in two dimensions is infinite dimensional, so the associated with the infinity of generators and infinity conserved charges provided. Is ...