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

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 β-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.