Abstract
L∞ 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 L3 algebra and when one considers dynamics the former is exactly promoted to an L4 algebra. The present computations show the fully algebraic structure of the fundamental charged heterotic string and the {L}_3^{mathrm{gauge}} structure of (Bosonic) Enhanced Double Field Theory.
Highlights
The DFT approach in metric formalismThe generalized Kerr-Schild ansatz (GKSA) is given by an exact and linear perturbation of the generalized background metric HMN
O(D, D + n) as global duality group, where n is the dimension of a gauge group
In this work we show that Gauged Double Field Theory (GDFT) can be cast in an L∞ structure
Summary
The GKSA is given by an exact and linear perturbation of the generalized background metric HMN 2D − 1) and an exact perturbation of the generalized background dilaton do. The perturbation of the generalized background metric HMN is given by a pair of generalized vectors, KM and KM , and an order parameter κ, such that. Equivalently, HMN KM KN = HMN KM KN = HMN KM KN = 0. The generalized background dilaton do is perturbed in a similar way,. The generalized metric HMN and the generalized background metric HMN are tensors with ω = 0 with respect to generalized diffeomorphisms, and ω(e−2d) = ω(e−2do) = 1. +4∂M HMN ∂N d − 4HMN ∂M d∂N d − ∂M ∂N HMN = 0
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