Deforming Soft Algebras for Gauge Theory

TL;DR

This paper explores how soft symmetry algebras in gauge theories are deformed by higher-dimensional corrections, revealing a non-abelian structure and new central extensions influenced by scalar field backgrounds.

Contribution

It introduces a novel deformation of the soft gauge symmetry algebra in gauge theory, incorporating scalar generators and central extensions, expanding the understanding of symmetry structures.

Findings

Soft algebra is deformed to a non-abelian associative algebra.

Central extensions are generated by scalar background shifts.

Deformations can be realized via shockwave scalar backgrounds.

Abstract

Symmetry algebras deriving from towers of soft theorems can be deformed by a short list of higher-dimension Wilsonian corrections to the effective action. We study the simplest of these deformations in gauge theory arising from a massless complex scalar coupled to $F^2$. The soft gauge symmetry '$s$-algebra', compactly realized as a higher-spin current algebra acting on the celestial sphere, is deformed and enlarged to an associative algebra containing soft scalar generators. This deformed soft algebra is found to be non-abelian even in abelian gauge theory. A two-parameter family of central extensions of the $s$-subalgebra are generated by shifting and decoupling the scalar generators. It is shown that these central extensions can also be generated by expanding around a certain non-trivial but Lorentz invariant shockwave type background for the scalar field.