Constraining subleading soft gluon and graviton theorems

TL;DR

This paper demonstrates that subleading soft gluon and graviton theorems are highly constrained by fundamental symmetries and consistency conditions, fixing their form up to a few parameters, especially in four dimensions.

Contribution

It provides a systematic derivation of the form of subleading soft theorems using elementary symmetry and consistency arguments, clarifying their universal structure.

Findings

Subleading soft operators are fixed by Poincaré and gauge invariance.

In four dimensions, the operators are completely determined by Lorentz symmetry.

The polarization part is fixed up to a single numerical factor per hard leg.

Abstract

We show that the form of the recently proposed subleading soft graviton and gluon theorems in any dimension are severely constrained by elementary arguments based on Poincar\'e and gauge invariance as well as a self-consistency condition arising from the distributional nature of scattering amplitudes. Combined with the assumption of a local form as it would arise from a Ward identity the orbital part of the subleading operators is completely fixed by the leading universal Weinberg soft pole behavior. The polarization part of the differential subleading soft operators in turn is determined up to a single numerical factor for each hard leg at every order in the soft momentum expansion. In four dimensions, factorization of the Lorentz group allows to fix the subleading operators completely.