On Loop Corrections to Subleading Soft Behavior of Gluons and Gravitons

TL;DR

This paper investigates loop corrections to the subleading soft behavior of gluons and gravitons, revealing anomalies at certain loop levels and proposing a new momentum-conservation approach for defining soft limits.

Contribution

It demonstrates that subleading soft behaviors are anomalous at loop levels and introduces a new momentum-conservation prescription for analyzing these effects.

Findings

Leading soft behavior remains uncorrected by loops.

Subleading soft behavior is anomalous at certain loop levels.

No new corrections beyond specified loop orders for subleading terms.

Abstract

Cachazo and Strominger recently proposed an extension of the soft-graviton theorem found by Weinberg. In addition, they proved the validity of their extension at tree level. This was motivated by a Virasoro symmetry of the gravity S-matrix related to BMS symmetry. As shown long ago by Weinberg, the leading behavior is not corrected by loops. In contrast, we show that with the standard definition of soft limits in dimensional regularization, the subleading behavior is anomalous and modified by loop effects. We argue that there are no new types of corrections to the first subleading behavior beyond one loop and to the second subleading behavior beyond two loops. To facilitate our investigation, we introduce a new momentum-conservation prescription for defining the subleading terms of the soft limit. We discuss the loop-level subleading soft behavior of gauge-theory amplitudes before turning to gravity amplitudes.