Deforming soft algebras for gauge theory

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