Homotopy representations of extended holomorphic symmetry in holomorphic twists

Abstract

We argue that holomorphic twists of supersymmetric field theories naturally come with a symmetry $L_{\infty }$-algebra that nontrivially extends holomorphic symmetry. This symmetry acts on spacetime fields only up to homotopy, and the extension is only visible at the level of higher components of the action. We explicitly compute this for the holomorphic twist of ten-dimensional supersymmetric Yang–Mills theory, which produces a nontrivial action of a higher $L_{\infty }$-algebra on (a graded version) of five-dimensional affine space.