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 (33)

• On BMS Invariance of Gravitational Scattering
• BMS supertranslations and Weinberg's soft graviton theorem
• Flat Space Amplitudes and Conformal Symmetry of the Celestial Sphere
• A Conformal Basis for Flat Space Amplitudes
• Light-ray operators in conformal field theory
• Lectures on Celestial Amplitudes
• A 2D Stress Tensor for 4D Gravity
• Holographic Symmetry Algebras for Gauge Theory and Gravity
• 4D Scattering Amplitudes and Asymptotic Symmetries from 2D CFT
• A Stereoscopic Look into the Bulk
• 2D Kac-Moody Symmetry of 4D Yang-Mills Theory
• On Loop Corrections to Subleading Soft Behavior of Gluons and Gravitons
• Conformally Soft Theorem in Gauge Theory
• Celestial amplitudes and conformal soft theorems
• Magnetic Corrections to the Soft Photon Theorem
• Conformally Soft Theorem In Gravity
• Soft Photon and Graviton Theorems in Effective Field Theory
• Conformal Blocks for Arbitrary Spins in Two Dimensions
• Celestial Amplitudes: Conformal Partial Waves and Soft Limits
• Infinite Set of Soft Theorems in Gauge-Gravity Theories as Ward-Takahashi Identities
• Loop-Corrected Virasoro Symmetry of 4D Quantum Gravity
• Extended Super BMS Algebra of Celestial CFT
• MHV Graviton Scattering Amplitudes and Current Algebra on the Celestial Sphere
• Soft Factorization in QED from 2D Kac-Moody Symmetry
• Celestial Diamonds: Conformal Multiplets in Celestial CFT
• MHV Gluon Scattering Amplitudes from Celestial Current Algebras
• Primary Fields in Celestial CFT
• A $d$-Dimensional Stress Tensor for Mink${}_{d+2}$ Gravity
• Celestial Current Algebra from Low's Subleading Soft Theorem
• Infinite Soft Theorems from Gauge Symmetry
• On Sugawara construction on Celestial Sphere
• Celestial superamplitude in $\mathcal{N}=4$ SYM theory
• Resolving the Weinberg Paradox with Topology

Cited by in corpus (22)

• Celestial Operator Product Expansions and ${\mathrm{w}}_{1+\infty }$ Symmetry for All Spins
• The SAGEX Review on Scattering Amplitudes, Chapter 11: Soft Theorems and Celestial Amplitudes
• Celestial operator products from the worldsheet
• Goldilocks Modes and the Three Scattering Bases
• Celestial $w_{1+\infty }$ Symmetries from Twistor Space
• From Celestial Correlators to AdS, and back
• 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