$E_2L_\infty$-algebras, Generalized Geometry, and Tensor Hierarchies

TL;DR

This paper introduces $E_2L_inf$-algebras, a new algebraic structure that unifies generalized geometry, double field theory symmetries, and tensor hierarchies in gauged supergravity, providing a higher gauge theory perspective.

Contribution

It defines $E_2L_inf$-algebras and demonstrates their role as the natural algebraic framework for various advanced geometric and physical theories, offering new insights into gauge symmetries and algebra integration.

Findings

$E_2L_inf$-algebras unify structures in generalized geometry and double field theory.

They provide a mathematical framework for tensor hierarchies in supergravity.

The approach offers a path to finite gauge transformations and non-local descriptions.

Abstract

We define a generalized form of $L_\infty$-algebras called $E_2L_\infty$-algebras. As we show, these provide the natural algebraic framework for generalized geometry and the symmetries of double field theory as well as the gauge algebras arising in the tensor hierarchies of gauged supergravity. Our perspective shows that the kinematical data of the tensor hierarchy is an adjusted higher gauge theory, which is important for developing finite gauge transformations as well as non-local descriptions. Mathematically, $E_2L_\infty$-algebras shed some light on Loday's problem of integrating Leibniz algebras.