Generalized Metric Formulation of Double Field Theory on Group Manifolds

TL;DR

This paper extends Double Field Theory on group manifolds by formulating a generalized metric approach, deriving field equations, and connecting it to traditional DFT and flux formulations, accounting for non-trivial backgrounds.

Contribution

It provides a generalized metric formulation of DFT on group manifolds, including all orders in fields and clarifies its relation to standard DFT and flux formulations.

Findings

Derived the generalized curvature scalar and Ricci tensor for DFT on group manifolds.

Proved invariance of the action under generalized and 2D diffeomorphisms.

Established the relation between DFT${}_\mathrm{WZW}$ and original DFT formulations.

Abstract

We rewrite the recently derived cubic action of Double Field Theory on group manifolds [arXiv:1410.6374] 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 diffeomorphisms and 2D-diffeomorphisms. Imposing additional constraints relating the background and fluctuations around it, the precise relation between the proposed generalized metric formulation of DFT${}_\mathrm{WZW}$ and of original DFT from tori is clarified. Furthermore we show how to relate DFT${}_\mathrm{WZW}$ of the WZW background with the flux formulation of original DFT.