Gauged Double Field Theory as an $L_{\infty}$ algebra

TL;DR

This paper explores the algebraic structure of Gauged Double Field Theory using $L_{}$ algebras, revealing a hierarchy from $L_3$ to $L_4$ that encodes the theory's symmetries and dynamics.

Contribution

It provides a detailed $L_{}$ algebraic formulation of Gauged Double Field Theory, including the off-shell and on-shell structures, and connects these to string theory frameworks.

Findings

Off-shell structure forms an $L_3$ algebra.

On-shell dynamics promote it to an $L_4$ algebra.

Reveals algebraic structure of heterotic string and enhanced DFT.

Abstract

$L_{\infty}$ algebras describe the underlying algebraic structure of many consistent classical field theories. In this work we analyze the algebraic structure of Gauged Double Field Theory in the generalized flux formalism. The symmetry transformations consist of a generalized deformed Lie derivative and Double Lorentz transformations. We obtain all the non-trivial products in a closed form considering a Generalized Kerr-Schild ansatz for the generalized frame and we include a linear perturbation for the generalized dilaton. The off-shell structure can be cast in an $L_{3}$ algebra and when one considers dynamics the former is exactly promoved to an $L_{4}$ algebra. The present computations show the fully algebraic structure of the fundamental charged heterotic string and the $L^{\rm{gauge}}_{3}$ structure of (Bosonic) Enhanced Double Field Theory.