Higher Symmetries in Twisted Eleven-Dimensional Supergravity
Fabian Hahner, Natalie M. Paquette, Surya Raghavendran
TL;DR
This work demonstrates that the residual symmetries of twisted eleven-dimensional supergravity acquire higher $L_ abla$-structures under both maximal and minimal twists. Using homotopy transfer and minimal-model techniques, the authors construct explicit $L_ abla$ maps from the twisted residual algebra to the BV-BRST field spaces, revealing nontrivial higher brackets (e.g., four-ary operations) that depend on geometric data like a $G_2$-structure. They show the maximal twist yields a Poisson–Chern–Simons-type minimal model with an inner action on component fields, while the minimally twisted theory links to the infinite-dimensional $E(5|10)$-type symmetry and its central extension. The results illuminate how higher symmetries organize protected sectors and potentially constrain BPS amplitudes and twisted holography in M-theory, and they establish a precise framework for comparing twisted residual algebras with the full physical fields through explicit homotopy-transfer maps.
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.