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

K. B. Alkalaev; Semyon Mandrygin

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arXiv · 2407.01741

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

K. B. Alkalaev·Semyon Mandrygin

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Abstract

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.

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K. B. Alkalaev, Semyon Mandrygin. 2024-07-01. One-point thermal conformal blocks from four-point conformal integrals. https://arxiv.org/abs/2407.01741

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