arXiv 2108.087992021-08hep-th

全息手征代数：超对称性、无限沃德恒等式和EFT

Holographic Chiral Algebra: Supersymmetry, Infinite Ward Identities, and EFTs

Hongliang Jiang

DOI：: 10.1007/JHEP01(2022)113

摘要：

天体全息术很有希望地根据天体的共形场论在零无穷远处重新表述散射振幅。最近，在Einstein-Yang-Mills理论中发现了一个无限维对称代数。推导的出发点是两个软流的天体OPE，关键成分是OPE中$\overline{SL(2,\mathbb R)}$子体之和。本文研究了超对称Einstein-Yang-Mills理论，得到了全息对称代数的超对称扩张。此外，我们推导出无限多个沃德恒等式与产生全息对称代数的无限软电流。这是通过考虑软对称电流和硬算子之间的OPE，然后对其$\overline{SL(2,\mathbb R)}$后代求和来实现的。这些沃德恒等式再现了已知的沃德恒等式，对应于主导、次主导和次-次主导软引力子定理以及主导和次主导软胶子定理.通过阴影变换，我们还得到了无穷多个阴影沃德恒等式，包括次主导软引力子的应力张量沃德恒等式。最后，我们用我们的方法讨论了对有效场论（EFT）中沃德恒等式的修正，再现了对引力子次次领先阶和光子次领先阶的软定理的修正.为此，我们推导了三个自旋无质量粒子立方相互作用的天体OPE和相应的沃德恒等式的一般公式。因此，我们的形式提供了一个统一的框架，了解沃德恒等式在天体共形场论，或等价的软定理在散射振幅。

英文摘要：

Celestial holography promisingly reformulates the scattering amplitude holographically in terms of celestial conformal field theory living at null infinity. Recently, an infinite-dimensional symmetry algebra was discovered in Einstein-Yang-Mills theory. The starting point in the derivation is the celestial OPE of two soft currents, and the key ingredient is the summation of $\overline{SL(2,\mathbb R)}$ descendants in OPE. In this paper, we consider the supersymmetric Einstein-Yang-Mills theory and obtain the supersymmetric extension of the holographic symmetry algebra. Furthermore, we derive infinitely many Ward identities associated with the infinite soft currents which generate the holographic symmetry algebra. This is realized by considering the OPE between a soft symmetry current and a hard operator, and then summing over its $\overline{SL(2,\mathbb R)}$ descendants. These Ward identities reproduce the known Ward identities corresponding to the leading, sub-leading, and sub-sub-leading soft graviton theorems as well as the leading and sub-leading soft gluon theorems. By performing shadow transformations, we also obtain infinitely many shadow Ward identities, including the stress tensor Ward identities for sub-leading soft graviton. Finally, we use our procedure to discuss the corrections to Ward identities in effective field theory (EFT), and reproduce the corrections to soft theorems at sub-sub-leading order for graviton and sub-leading order for photon. For this aim, we derive general formulae for the celestial OPE and its corresponding Ward identities arising from a cubic interaction of three spinning massless particles. Our formalism thus provides a unified framework for understanding the Ward identities in celestial conformal field theory, or equivalently the soft theorems in scattering amplitude.

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