Homotopy representations of extended holomorphic symmetry in holomorphic twists

TL;DR

This paper explores how holomorphic twists of supersymmetric theories inherently involve extended symmetries described by higher $L_ abla$-algebras, revealing new algebraic structures acting on spacetime fields up to homotopy.

Contribution

It explicitly computes the extended $L_ abla$-symmetry in the holomorphic twist of 10D supersymmetric Yang-Mills theory, demonstrating the nontrivial higher algebraic action.

Findings

Identifies a natural $L_ abla$-algebra extension in holomorphic twists.

Explicitly computes the higher symmetry for 10D SYM.

Shows the symmetry acts on fields up to homotopy.

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.