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.

26 pages. Added additional references and minor clarifications

References in corpus (6)

• Superfield actions for N=8 and N=6 conformal theories in three dimensions
• Loop Amplitudes and Quantum Homotopy Algebras
• SU(5)-invariant decomposition of ten-dimensional Yang-Mills supersymmetry
• Perspectives on the pure spinor superfield formalism
• Homotopy algebra of open-closed strings
• The Derived Pure Spinor Formalism as an Equivalence of Categories