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

References in corpus (12)

• Evidence for a New Soft Graviton Theorem
• Gluon Amplitudes as 2d Conformal Correlators
• 4D Scattering Amplitudes and Asymptotic Symmetries from 2D CFT
• Loop Corrections to Soft Theorems in Gauge Theories and Gravity
• Symmetries of Celestial Amplitudes
• Gravity from Rational Curves
• A simple formula for gravitational MHV amplitudes
• From Scattering Amplitudes to Classical Physics: Universality, Double Copy and Soft Theorems
• A "Twistor String" Inspired Formula For Tree-Level Scattering Amplitudes in N=8 SUGRA
• Simplicity in AdS Perturbative Dynamics
• Resultants and Gravity Amplitudes
• New Formulae for Gravity Amplitudes: Parity Invariance and Soft Limits