Loop Corrections to Soft Theorems in Gauge Theories and Gravity

TL;DR

This paper investigates loop corrections to the new soft theorems in gauge theories and gravity, confirming their validity at one loop for certain amplitudes and identifying specific corrections for others using recursion relations.

Contribution

It provides the first all-multiplicity one-loop corrections to subleading soft theorems in Yang-Mills theory and clarifies the role of double-pole contributions in loop corrections.

Findings

Subleading soft theorems are exact for all-plus amplitudes at one loop.

Loop corrections are necessary for plus-helicity single-minus amplitudes.

Recursion relations reveal the source of soft theorem mismatches in loop amplitudes.

Abstract

In this paper, we study loop corrections to the recently proposed new soft theorem of Cachazo-Strominger, for both gravity and gauge theory amplitudes. We first review the proof of its tree-level validity based on BCFW recursion relations, which also establishes an infinite series of universals soft functions for MHV amplitudes, and a generalization to supersymmetric cases. For loop corrections, we focus on infrared finite, rational amplitudes at one loop, and apply recursion relations with boundary or double-pole contributions. For all-plus amplitudes, we prove that the subleading soft-theorems are exact to all multiplicities for both gauge and gravity amplitudes. For single-minus amplitudes, while the subleading soft-theorems are again exact for the minus-helicity soft leg, for plus-helicity loop corrections are required. Using recursion relations, we identify the source of such mismatch as stemming from the special contribution containing double poles, and obtain the all-multiplicity one-loop corrections to the subleading soft behavior in Yang-Mills theory. We also comment on the derivation of soft theorems using BCFW recursion in arbitrary dimensions.