# Higher Gauge Structures in Double and Exceptional Field Theory

## TL;DR

This paper reviews the formulation of higher gauge symmetries in double and exceptional field theories using an embedding tensor approach, revealing their underlying algebraic structures such as Leibniz and L-infinity algebras.

## Contribution

It introduces a unified algebraic framework for gauge symmetries in these theories based on embedding tensors and infinite-dimensional Lie algebras.

## Key findings

- Embedding tensor maps from representation space to Lie algebra.
- Lie algebra induces Leibniz--Loday algebra on the representation.
- Gauge structures fit into an L-infinity algebra framework.

## Abstract

We review the higher gauge symmetries in double and exceptional field theory from the viewpoint of an embedding tensor construction. This is based on a (typically infinite-dimensional) Lie algebra $\frak{g}$ and a choice of representation $R$. The embedding tensor is a map from the representation space $R$ into $\frak{g}$ satisfying a compatibility condition (`quadratic constraint'). The Lie algebra structure on $\frak{g}$ is transported to a Leibniz--Loday algebra on $R$, which in turn gives rise to an $L_{\infty}$-structure. We review how the gauge structures of double and exceptional field theory fit into this framework.