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

TL;DR

<3-5 sentence high-level summary> This work extends celestial holography by constructing a supersymmetric holographic chiral algebra for SUSY EYM and deriving an infinite set of Ward identities from soft currents, including shadow versions. The approach hinges on summing over $ar{SL}(2,bR)$ descendants in soft OPEs and projecting onto holomorphic chiral currents, revealing a $w_{1+ obreak imes obreak ext{infty}}$-type algebra generated by leading soft gravitons and gluons, with SUSY links to gravitinos and gluinos. It also derives general OPEs from cubic EFT vertices and shows EFT corrections to Ward identities appear at sub-leading orders for photons and sub-sub-leading for gravitons, while the holographic chiral algebra remains robust in the positive-helicity sector. The framework thus unifies soft theorems and celestial Ward identities, providing a path to explore loop corrections, higher dimensions, and multiple-soft insertions within a holographic CCFT setting.

Abstract

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.