Asymptotic Symmetries for Logarithmic Soft Theorems in Gauge Theory and Gravity

TL;DR

This paper explores the connection between logarithmic soft theorems in gauge theory and gravity and their underlying asymptotic symmetries, providing a symmetry-based understanding of loop corrections in infrared physics.

Contribution

It initiates a program to compute infrared corrections to asymptotic charges, linking logarithmic soft theorems to symmetry principles in quantum gauge and gravity theories.

Findings

Derived finite charge conservation laws for infrared dressings.

Showed that logarithmic soft theorems correspond to symmetry charges at all loop orders.

Established a universal symmetry interpretation for logarithmic soft theorems.

Abstract

Gauge theories and perturbative gravity in four dimensions are governed by a tower of infinite-dimensional symmetries which arise from tree-level soft theorems. However, aside from the leading soft theorems which are all-loop exact, subleading ones receive loop corrections due to long-range infrared effects which result in new soft theorems with logarithmic dependence on the energy of the soft particle. The conjectured universality of these logarithmic soft theorems to all loop orders cries out for a symmetry interpretation. In this letter we initiate a program to compute long-range infrared corrections to the charges that generate the asymptotic symmetries in (scalar) QED and perturbative gravity. For late-time fall-offs of the electromagnetic and gravitational fields which give rise to infrared dressings for the matter fields, we derive finite charge conservation laws and show that in the quantum theory they correspond precisely to the first among the infinite tower of logarithmic soft theorems. This symmetry interpretation, by virtue of being universal and all-loop exact, is a key element for a holographic principle in spacetimes with flat asymptotics.