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

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.

arXiv comment71 pages, published in JHEP

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• Hidden-Charm Tetraquarks in a Mixture Model: Coupled-Channel Analysis with $c\bar{c}$ and Hadronic Molecular Components
• On the $L_{\infty }$ formulation of Chern-Simons theories