Closed-form expression for cross-channel conformal blocks near the lightcone
Closed-form expression for cross-channel conformal blocks near the lightcone
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DOI：
10.1007/jhep01(2020)055
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发表时间：
2019-06
影响因子：
5.4
通讯作者：
Wenliang Li
中科院分区：
文献类型：
--
作者：
Wenliang Li
在共形场论的研究中，光锥极限中的共形块是解析共形自举法的基础。这里我们考虑通用标量原色的 4 点函数的光锥极限。基于洛伦兹反演自旋的非微扰极结构，我们提出了跨通道共形块的自然基函数。在此新基础上，我们根据 Kampé de Fériet 函数找到了交叉共形块的闭合形式表达式，该表达式适用于一般维度中任意自旋的中间算子。我们推导出相同外部尺度尺寸情况下的一般洛伦兹反演。我们对光锥极限的结果也揭示了光锥扩展中共形块的完整分析结构。
In the study of conformal field theories, conformal blocks in the lightcone limit are fundamental to the analytic conformal bootstrap method. Here we consider the lightcone limit of 4-point functions of generic scalar primaries. Based on the nonperturbative pole structure in spin of Lorentzian inversion, we propose the natural basis functions for cross-channel conformal blocks. In this new basis, we find a closed-form expression for crossed conformal blocks in terms of the Kampé de Fériet function, which applies to intermediate operators of arbitrary spin in general dimensions. We derive the general Lorentzian inversion for the case of identical external scaling dimensions. Our results for the lightcone limit also shed light on the complete analytic structure of conformal blocks in the lightcone expansion.