A bi-invariant Einstein-Hilbert action for the non-geometric string. (English) Zbl 1372.83056
Summary: 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.
MSC:
| 83D05 | Relativistic gravitational theories other than Einstein’s, including asymmetric field theories |
| 83C10 | Equations of motion in general relativity and gravitational theory |
| 53Z05 | Applications of differential geometry to physics |
| 83E30 | String and superstring theories in gravitational theory |
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