Gauged double field theory as an L∞ algebra

A bstract L ∞ algebras describe the underlying algebraic structure of many consistent classical field theories. In this work we analyze Gauged Double Field Theory in generalized flux formalism. The symmetry transformations consist a deformed Lie derivative and double Lorentz transformations. We obtain all non-trivial products closed form considering Kerr-Schild ansatz for frame include linear perturbation dilaton. off-shell can be cast an 3 algebra when one considers dynamics former is exactly promoted to 4 algebra. present computations show fully fundamental charged heterotic string $$ {L}_3^{\mathrm{gauge}} L 3 gauge (Bosonic) Enhanced Theory.