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

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.

References in corpus (6)

• Lectures on Celestial Amplitudes
• Holographic Symmetry Algebras for Gauge Theory and Gravity
• 4D Scattering Amplitudes and Asymptotic Symmetries from 2D CFT
• On Loop Corrections to Subleading Soft Behavior of Gluons and Gravitons
• Celestial Diamonds: Conformal Multiplets in Celestial CFT
• Celestial superamplitude in $\mathcal{N}=4$ SYM theory

Cited by in corpus (22)

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• The SAGEX Review on Scattering Amplitudes, Chapter 11: Soft Theorems and Celestial Amplitudes
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• Black Holes in Klein Space
• Gauge independent kinematic algebra of self-dual Yang-Mills theory
• Four-point correlators of light-ray operators in CCFT
• All-order celestial OPE in the MHV sector
• Radiative phase space extensions at all orders in r for self-dual Yang-Mills and Gravity
• Celestial Supersymmetry
• Supersymmetric celestial OPEs and soft algebras from the ambitwistor string worldsheet
• Toward A Supersymmetric $w_{1+\infty }$ Symmetry in the Celestial Conformal Field Theory
• Lorentz Symmetry and IR Structure of The BFSS Matrix Model
• Celestial Mellin Amplitude
• The $\mathcal{N}=2$ Supersymmetric $w_{1+\infty }$ Symmetry in the Two-Dimensional SYK Models
• Deformed $w_{1+\infty }$ Algebras in the Celestial CFT
• Structure of deformed $w_{1+\infty }$ symmetry and topological generalization in Celestial CFT
• Currents in Celestial CFT
• The Structure of the $\mathcal{N}=4$ Supersymmetric Linear $W_{\infty }[\lambda ]$ Algebra
• $\widehat{s{l}_2}$ symmetry of ${\mathbb{R}}^{1,3}$ gravity