Sub-subleading Soft Graviton Theorem in Generic Theories of Quantum Gravity

Abstract

We analyze scattering amplitudes with one soft external graviton and arbitrary number of other finite energy external states carrying arbitrary mass and spin to sub-subleading order in the momentum of the soft graviton. Our result can be expressed as the sum of a universal part that depends only on the amplitude without the soft graviton and not the other details of the theory and a non-universal part that depends on the amplitude without the soft graviton, and the two and three point functions of the theory. For tree amplitudes our results are valid in all space-time dimensions while for loop amplitudes, infrared divergences force us to restrict our analysis to space time dimensions five or more. With this restriction the results are valid to all orders in perturbation theory. Our results agree with known results in quantum field theories and string theory.

52 pages, 7 figures v2: Proved that the non-universal sub-subleading corrections depend only on on-shell 3-point functions

References in corpus (12)

• Loop Corrections to Soft Theorems in Gauge Theories and Gravity
• A Periodic Table of Effective Field Theories
• Subleading soft theorem in arbitrary dimension from scattering equations
• The method of regions and next-to-soft corrections in Drell-Yan production
• Sub-subleading soft gravitons and large diffeomorphisms
• Diagrammatic insights into next-to-soft corrections
• Next-to-soft corrections to high energy scattering in QCD and gravity
• Next to subleading soft-graviton theorem in arbitrary dimensions
• Subleading Soft Factor for String Disk Amplitudes
• The Double Copy Structure of Soft Gravitons
• Soft behavior of a closed massless state in superstring and universality in the soft behavior of the dilaton
• Double Soft Theorem for Perturbative Gravity

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