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arXiv · 2212.08643

Deforming Soft Algebras for Gauge Theory

Walker Melton·Sruthi A. Narayanan·Andrew Strominger
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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.

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Walker Melton, Sruthi A. Narayanan, Andrew Strominger. 2022-12-16. Deforming Soft Algebras for Gauge Theory. https://doi.org/10.1007/jhep03(2023)233

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