Deforming Soft Algebras for Gauge Theory

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.

13 pages, 1 figure

References in corpus (3)

• Celestial holography on Kerr-Schild backgrounds
• On the associativity of 1-loop corrections to the celestial operator product in gravity
• Celestial Locality and the Jacobi Identity

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