Notes on Conformal Soft Theorems and Recursion Relations in Gravity

Abstract

Celestial amplitudes are flat-space amplitudes which are Mellin-transformed to correlators living on the celestial sphere. In this note we present a recursion relation, based on a tree-level BCFW recursion, for gravitational celestial amplitudes and use it to explore the notion of conformal softness. As the BCFW formula exponentiates in the soft energy, it leads directly to conformal soft theorems in an exponential form. These appear from a soft piece of the amplitude characterized by a discrete family of singularities with weights $\Delta =1-{\mathbb{Z}}_{+}$. As a byproduct, in the case of the MHV sector we provide a direct celestial analogue of Hodges' recursion formula at all multiplicities.

21+3 pages, 1 figure, comments are welcome

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Cited by in corpus (28)

• Lectures on Celestial Amplitudes
• Holographic Symmetry Algebras for Gauge Theory and Gravity
• Celestial amplitudes and conformal soft theorems
• Celestial Operator Product Expansions and ${\mathrm{w}}_{1+\infty }$ Symmetry for All Spins
• $(2,2)$ Scattering and the Celestial Torus
• MHV Graviton Scattering Amplitudes and Current Algebra on the Celestial Sphere
• Celestial Diamonds: Conformal Multiplets in Celestial CFT
• Shifting Spin on the Celestial Sphere
• MHV Gluon Scattering Amplitudes from Celestial Current Algebras
• Lectures on Celestial Holography
• Celestial operator products from the worldsheet
• Goldilocks Modes and the Three Scattering Bases
• Ambidextrous light transforms for celestial amplitudes
• UV considerations on scattering amplitudes in a web of theories
• On loop celestial amplitudes for gauge theory and gravity
• Celestial $w_{1+\infty }$ Symmetries from Twistor Space
• Relativistic partial waves for celestial amplitudes
• Celestial Dual Superconformal Symmetry, MHV Amplitudes and Differential Equations
• Subsubleading soft graviton symmetry and MHV graviton scattering amplitudes
• Celestial Superamplitudes
• Conformally Soft Fermions
• (Chiral) Virasoro invariance of the tree-level MHV graviton scattering amplitudes
• Celestial $w_{1+\infty }$ charges and the subleading structure of asymptotically-flat spacetimes
• Deformed $w_{1+\infty }$ Algebras in the Celestial CFT
• $p$-Forms on the Celestial Sphere
• Celestial IR divergences and the effective action of supertranslation modes
• Celestial OPE blocks
• Celestial Holography