Higher Symmetries in Twisted Eleven-Dimensional Supergravity

TL;DR

This paper demonstrates that higher symmetries emerge in twisted eleven-dimensional supergravity, transforming residual super-Poincaré symmetries into complex algebraic structures, revealing new insights into the theory's symmetry properties.

Contribution

It extends the understanding of residual symmetries in twisted supergravity, showing they form $L_$ algebras with non-strict actions, applicable to eleven-dimensional supergravity.

Findings

Residual symmetries form $L_$ algebras in twisted supergravity

Higher corrections modify super-Poincaré symmetries

Detailed connection between physical and twisted fields

Abstract

In supersymmetric theories, protected quantities can be reorganized into holomorphic-topological theories by twisting. Recently, it was observed by Jonsson, Kim and Young that residual super-Poincar\'e symmetries in certain twisted theories can receive higher corrections, turning them into $L_\infty$ algebras with non-strict actions on the twisted fields. In this note, we show that the same phenomenon occurs for the two admissible twists of eleven-dimensional supergravity. Along the way, we discuss in detail the connection between components of physical and twisted fields.