One-point thermal conformal blocks from four-point conformal integrals

We develop the thermal shadow formalism to study the conformal blocks decomposition in \(D\)-dimensional conformal field theory on \(\mathbb{S}_{\beta}^{1} \times \mathbb{S}^{D-1}\), where the temperature is \(T = \beta^{-1}\). It is demonstrated that both the 1-point thermal (\(T\neq 0\)) conformal...

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Bibliographic Details
Published inarXiv.org
Main Authors Alkalaev, K B, Mandrygin, Semyon
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 31.10.2024
Subjects
Field theory
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Summary:We develop the thermal shadow formalism to study the conformal blocks decomposition in \(D\)-dimensional conformal field theory on \(\mathbb{S}_{\beta}^{1} \times \mathbb{S}^{D-1}\), where the temperature is \(T = \beta^{-1}\). It is demonstrated that both the 1-point thermal (\(T\neq 0\)) conformal blocks and the 4-point plane (\(T=0\)) conformal blocks are defined by the same 4-point conformal integral. It is shown that up to power prefactors the 1-point thermal conformal block is given by the fourth Appell function.
ISSN:2331-8422