Gravitational soft theorem from emergent soft gauge symmetries

TL;DR

This paper derives the gravitational soft theorem up to sub-subleading order using effective Lagrangians, revealing the role of emergent soft gauge symmetries in universality and providing a Lagrangian-based operatorial formulation.

Contribution

It presents a novel derivation of the gravitational soft theorem at sub-subleading power from the effective Lagrangian perspective, emphasizing the role of emergent soft gauge symmetries.

Findings

Soft graviton emission is universal up to sub-subleading power.

Emergent soft gauge symmetries explain differences between gravitational and gauge boson emissions.

Operatorial form of soft theorems derived directly at the Lagrangian level.

Abstract

We consider and derive the gravitational soft theorem up to the sub-subleading power from the perspective of effective Lagrangians. The emergent soft gauge symmetries of the effective Lagrangian provide a transparent explanation of why soft graviton emission is universal to sub-subleading power, but gauge boson emission is not. They also suggest a physical interpretation of the form of the soft factors in terms of the charges related to the soft transformations and the kinematics of the multipole expansion. The derivation is done directly at Lagrangian level, resulting in an operatorial form of the soft theorems. In order to highlight the differences and similarities of the gauge-theory and gravitational soft theorems, we include an extensive discussion of soft gauge-boson emission from scalar, fermionic and vector matter at subleading power.