MHV Graviton Scattering Amplitudes and Current Algebra on the Celestial Sphere

Abstract

The Cachazo-Strominger subleading soft graviton theorem for a positive helicity soft graviton is equivalent to the Ward identities for $\overline{SL(2,\mathbb{C})}$ currents. This naturally gives rise to a $\overline{SL(2,\mathbb{C})}$ current algebra living on the celestial sphere. The generators of the $\overline{SL(2,\mathbb{C})}$ current algebra and the supertranslations, coming from a positive helicity leading soft graviton, form a closed algebra. We find that the OPE of two graviton primaries in the Celestial CFT, extracted from MHV amplitudes, is completely determined in terms of this algebra. To be more precise, 1) The subleading terms in the OPE are determined in terms of the leading OPE coefficient if we demand that both sides of the OPE transform in the same way under this local symmetry algebra. 2) Positive helicity gravitons have null states under this local algebra whose decoupling leads to differential equations for MHV amplitudes. An $n$ point MHV amplitude satisfies two systems of $(n-2)$ linear first order PDEs corresponding to $(n-2)$ positive helicity gravitons. We have checked, using Hodges' formula, that one system of differential equations is satisfied by any MHV amplitude, whereas the other system has been checked up to six graviton MHV amplitude. 3) One can determine the leading OPE coefficients from these differential equations. This points to the existence of an autonomous sector of the Celestial CFT which holographically computes the MHV graviton scattering amplitudes and is completely defined by this local symmetry algebra. The MHV-sector of the Celestial CFT is like a minimal model of $2$-D CFT.

Final JHEP Version

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Cited by in corpus (42)

• Lectures on Celestial Amplitudes
• Holographic Symmetry Algebras for Gauge Theory and Gravity
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• Celestial Operator Product Expansions and ${\mathrm{w}}_{1+\infty }$ Symmetry for All Spins
• AdS Witten Diagrams to Carrollian Correlators
• Celestial Diamonds: Conformal Multiplets in Celestial CFT
• Carrollian Approach to $1+3$D Flat Holography
• The SAGEX Review on Scattering Amplitudes, Chapter 11: Soft Theorems and Celestial Amplitudes
• Revisiting the Conformally Soft Sector with Celestial Diamonds
• MHV Gluon Scattering Amplitudes from Celestial Current Algebras
• Gravity from symmetry: Duality and impulsive waves
• Celestial operator products from the worldsheet
• Loops on the Celestial Sphere
• Holographic Chiral Algebra: Supersymmetry, Infinite Ward Identities, and EFTs
• Coadjoint representation of the BMS group on celestial Riemann surfaces
• Ambidextrous light transforms for celestial amplitudes
• Celestial double copy from the worldsheet
• Descendants in celestial CFT and emergent multi-collinear factorization
• Celestial Dual Superconformal Symmetry, MHV Amplitudes and Differential Equations
• From Celestial Correlators to AdS, and back
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• The structure of IR divergences in celestial gluon amplitudes
• All-order celestial OPE in the MHV sector
• Soft Gravity by Squaring Soft QED on the Celestial Sphere
• Conformally Soft Fermions
• Revisiting the Shadow Stress Tensor in Celestial CFT
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• Celestial Recursion
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• Supersymmetric celestial OPEs and soft algebras from the ambitwistor string worldsheet
• Celestial insights into the S-matrix bootstrap
• All-order celestial OPE from on-shell recursion
• w(1+infinity) and the Celestial Sphere
• Zwanziger's pairwise little group on the celestial sphere
• Non-Lorentzian Kač-Moody Algebras
• Soft photon radiation and entanglement
• A Celestial Route to AdS Bulk Locality
• $\widehat{s{l}_2}$ symmetry of ${\mathbb{R}}^{1,3}$ gravity
• Celestial OPE blocks
• Celestial Holography