# Soft charges from the geometry of field space

## TL;DR

This paper introduces a geometric framework in field space to derive soft charges in gauge theories, clarifying their origin and symmetry properties, and explaining the finite versus infinite symmetry enhancements at infinity.

## Contribution

It provides a gauge-invariant, geometric derivation of soft charges that unifies finite and infinite regions and offers insights into magnetic charges from spacetime covariance.

## Key findings

- Soft charges are derived from a geometric framework in field space.
- The formalism explains the finite versus infinite symmetry enhancement.
- A proposal for magnetic charges based on Lorentz covariance is introduced.

## Abstract

Infinite sets of asymptotic soft-charges were recently shown to be related to new symmetries of the $S$-matrix, spurring a large amount of research on this and related questions. Notwithstanding, the raison-d'\^etre of these soft-charges rests on less firm ground, insofar as their known derivations through generalized Noether procedures tend to rely on the fixing of (gauge-breaking) boundary conditions rather than on manifestly gauge-invariant computations. In this article, we show that a geometrical framework anchored in the space of field configurations singles out the known leading-order soft charges in gauge theories. Our framework unifies the treatment of finite and infinite regions, and thus it explains why the infinite enhancement of the symmetry group is a property of asymptotic null infinity and should not be expected to hold within finite regions, where at most a finite number of physical charges -- corresponding to the reducibility parameters of the quasi-local field configuration -- is singled out. As a bonus, our formalism also suggests a simple proposal for the origin of magnetic-type charges at asymptotic infinity based on spacetime (Lorentz) covariance rather than electromagnetic duality.