Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 21 (2025), 100, 30 pages      arXiv:2506.02246      https://doi.org/10.3842/SIGMA.2025.100

Higher Symmetries in Twisted Eleven-Dimensional Supergravity

Fabian Hahner a, Natalie M. Paquette a and Surya Raghavendran bc
a) Department of Physics, University of Washington, 3910 15th Ave NE, Seattle, WA 98195, USA
b) Department of Mathematics, Yale University, P.O. Box 208283, New Haven, CT 06520, USA
c) School of Mathematics, University of Edinburgh, Peter Guthrie Tait Road, King's Buildings, Edinburgh, EH9 3FD, UK

Received July 09, 2025, in final form November 25, 2025; Published online December 03, 2025

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-Poincaré 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.

Key words: twisted supergravity; higher symmetry; $L_\infty$ algebra; topological-holomorphic field theory.

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