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arXiv · 1211.0030

Non-geometric strings, symplectic gravity and differential geometry of Lie algebroids

Ralph Blumenhagen·Andreas Deser·Erik Plauschinn·Felix Rennecke
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Abstract

Based on the structure of a Lie algebroid for non-geometric fluxes in string theory, a differential-geometry calculus is developed which combines usual diffeomorphisms with so-called β-diffeomorphisms emanating from gauge symmetries of the Kalb-Ramond field. This allows to construct a bi-invariant action of Einstein-Hilbert type comprising a metric, a (quasi-)symplectic structure βand a dilaton. As a salient feature, this symplectic gravity action and the resulting equations of motion take a form which is similar to the standard action and field equations. Furthermore, the two actions turn out to be related via a field redefinition reminiscent of the Seiberg-Witten limit. Remarkably, this redefinition admits a direct generalization to higher-order α'-corrections and to the additional fields and couplings appearing in the effective action of the superstring. Simple solutions to the equations of motion of the symplectic gravity action, including Calabi-Yau geometries, are discussed.

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Ralph Blumenhagen, Andreas Deser, Erik Plauschinn, Felix Rennecke. 2013-04-15. Non-geometric strings, symplectic gravity and differential geometry of Lie algebroids. https://doi.org/10.1007/jhep02(2013)122

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