Subleading Soft Graviton Theorem for Loop Amplitudes

Abstract

Superstring field theory gives expressions for heterotic and type II string loop amplitudes that are free from ultraviolet and infrared divergences when the number of non-compact space-time dimensions is five or more. We prove the subleading soft graviton theorem in these theories to all orders in perturbation theory for S-matrix elements of arbitrary number of finite energy external states but only one external soft graviton. We also prove the leading soft graviton theorem for arbitrary number of finite energy external states and arbitrary number of soft gravitons. Since our analysis is based on general properties of one particle irreducible effective action, the results are valid in any theory of quantum gravity that gives finite result for the S-matrix order by order in perturbation theory without violating general coordinate invariance.

LaTeX file, 20 pages; v2: added explanation for dropping terms involving Christoffel symbols from the covariant derivatives; v3: references updated, other minor changes

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• The SAGEX Review on Scattering Amplitudes, Chapter 11: Soft Theorems and Celestial Amplitudes
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• Background Independence of Closed Superstring Field Theory
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• Soft Theorems from Compactification
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• Leading soft theorem for multiple gravitini
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