# Generalized metric formulation of double field theory on group manifolds

Abstract: We rewrite the recently derived cubic action of Double Field Theory on group manifolds (1) in terms of a generalized metric and extrapolate it to all orders in the fields. For the resulting action, we derive the field equations and state them in terms of a generalized curvature scalar and a generalized Ricci tensor. Compared to the generalized metric formulation of DFT derived from tori, all these quantities receive additional contributions related to the non-trivial background. It is shown that the action is invariant under its generalized dieomorphisms and 2D-dieomorphisms . Imposing additional constraints relating the background and fluctuations around it, the precise relation between the proposed generalized metric formulation of DFTWZW and of original DFT from tori is clarified. Furthermore, we show how to relate DFTWZW of the WZW background with the flux formulation of original DFT.

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### "Generalized metric formulation of d..." refers background in this paper

...derivation [3] and it states that winding and momentum excitations in the same direction are not allowed....

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...The calculations shown in this subsection generalize in some sense the endeavor of [5] to find a background independent version of the cubic DFT action derived in [3]....

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### "Generalized metric formulation of d..." refers background in this paper

...In this case so called non-geometric backgrounds [12, 13, 16, 17] arise....

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