  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.
