A bi-invariant Einstein-Hilbert action for the non-geometric string

TL;DR

This paper introduces a new bi-invariant Einstein-Hilbert action in string theory that incorporates non-geometric fluxes and a dynamical symplectic structure, expanding the understanding of string effective actions.

Contribution

It develops a differential geometry framework combining diffeomorphisms with beta-diffeomorphisms to construct a bi-invariant gravitational action for non-geometric string backgrounds.

Findings

Formulation of a bi-invariant Einstein-Hilbert action for non-geometric fluxes

Derivation of equations of motion for symplectic gravity

Discussion of the relation to standard string effective actions

Abstract

Inspired by recent studies on string theory with non-geometric fluxes, we develop a differential geometry calculus combining usual diffeomorphisms with what we call beta-diffeomorphisms. This allows us to construct a manifestly bi-invariant Einstein-Hilbert type action for the graviton, the dilaton and a dynamical (quasi-)symplectic structure. The equations of motion of this symplectic gravity theory, further generalizations and the relation to the usual form of the string effective action are discussed. The Seiberg-Witten limit, known for open strings to relate commutative with non-commutative theories, makes an interesting appearance.