Loop Corrections to Soft Theorems in Gauge Theories and Gravity
Song He, Yu-tin Huang, Congkao Wen
TL;DR
The paper investigates loop corrections to the Cachazo-Strominger soft theorems for gauge theories and gravity by focusing on one-loop rational amplitudes (all-plus and single-minus). Using BCFW-like recursion with boundary and double-pole terms, it shows all-plus amplitudes satisfy the soft theorems exactly in both YM and gravity, while single-minus amplitudes exhibit corrections for holomorphic soft limits due to double-pole contributions, with explicit formulas and low-point checks. The results reveal that loop corrections are necessary for certain subleading soft terms, trace the source to double-pole effects, and hint at deeper structures such as higher-dimensional extensions, supersymmetric generalizations, and potential double-copy relations. The work clarifies the precise loop-level status of soft theorems and informs symmetry-based constraints on amplitudes across dimensions and theories.
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.