Low-Energy Behavior of Gluons and Gravitons from Gauge Invariance

TL;DR

This paper demonstrates that gauge invariance at tree level fully determines the first subleading soft-gluon and the first two subleading soft-graviton behaviors in n-point amplitudes across dimensions, with implications for loop corrections and BMS symmetry.

Contribution

It provides a gauge invariance-based proof for soft-gluon and soft-graviton behaviors, extending understanding of their universality and loop correction effects.

Findings

Tree-level gauge invariance determines soft behaviors in D dimensions.

Loop effects correct soft behaviors in four dimensions.

Scalar loops in gravitons affect only the second subleading order.

Abstract

We show that at tree level, on-shell gauge invariance can be used to fully determine the first subleading soft-gluon behavior and the first two subleading soft-graviton behaviors. Our proofs of the behaviors for n-gluon and n-graviton tree amplitudes are valid in D dimensions and are similar to Low's proof of universality of the first subleading behavior of photons. In contrast to photons coupling to massive particles, in four dimensions the soft behaviors of gluons and gravitons are corrected by loop effects. We comment on how such corrections arise from this perspective. We also show that loop corrections in graviton amplitudes arising from scalar loops appear only at the second soft subleading order. This case is particularly transparent because it is not entangled with graviton infrared singularities. Our result suggests that if we set aside the issue of infrared singularities, soft-graviton Ward identities of extended BMS symmetry are not anomalous through the first subleading order.