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arXiv 2407.01741hep-th
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来自四点共形积分的一点热共形块

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

K. B. Alkalaev, Semyon Mandrygin

备注：
18 pp, v2: misprints corrected, extended discussion in Section 2, more clarifying comments, references added; v3: extended discussion of the thermal conformal block in the high-temperature regime as well as at self-dual conformal dimensions; more detail on non-parametric conformal and thermal integrals and their relation to the Bloch-Wigner function in a new appendix A; refs added, journal version
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AI总结：

本研究发展热阴影形式研究D维共形场论的共形块分解，证明1点热共形块与4点零温平面共形块共享同一四点共形积分，且前者不计幂次 prefactor 时由第四类Appell函数给出。

摘要：

我们发展了热阴影形式体系，用于研究温度为$T = β^{-1}$的$\boldsymbol{\rm \bigcirc}_β^{1} \times \boldsymbol{\rm \bigcirc}^{D-1}$上$D$维共形场论中的共形块分解。研究表明，1点热（$T\neq 0$）共形块与4点平面（$T=0$）共形块由同一个四点共形积分定义。结果显示，不计幂次 prefactor 时，1点热共形块由第四类Appell函数给出。

英文摘要：

We develop the thermal shadow formalism to study the conformal blocks decomposition in $D$-dimensional conformal field theory on $\mathbb{S}_β^{1} \times \mathbb{S}^{D-1}$, where the temperature is $T = β^{-1}$. 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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