$L_\infty$ algebras and Tensor Hierarchies in Exceptional Field Theory and Gauged Supergravity

TL;DR

This paper demonstrates how tensor hierarchies in exceptional field theories can be described using $L_ abla$ algebras, revealing new symmetries and their relation to gauged supergravities.

Contribution

It introduces an $L_ abla$ algebra framework for tensor hierarchies in exceptional field theories, highlighting the role of covariantly constrained fields and new symmetry structures.

Findings

Tensor hierarchies fit into $L_ abla$ algebra structures.

Gauging-dependent parameters lead to trivial gauge transformations.

New symmetries emerge in gauged supergravities.

Abstract

We show how the gauge and field structure of the tensor hierarchies in Double and $E_{7(7)}$ Exceptional Field Theory fits into $L_\infty$ algebras. Special attention is paid to redefinitions, the role of covariantly constrained fields and intertwiners. The results are connected to Gauged Supergravities through generalized Scherk-Schwarz reductions. We find that certain gauging-dependent parameters generate trivial gauge transformations, giving rise to novel symmetries for symmetries that are absent in their ungauged counterparts.