Abstract
We summarize the global geometric formulation of Einstein-Scalar-Maxwell theories twisted by flat symplectic vector bundle which encodes the duality structure of the theory. We describe the scalar-electromagnetic symmetry group of such models, which consists of flat unbased symplectic automorphisms of the flat symplectic vector bundle lifting those isometries of the scalar manifold which preserve the scalar potential. The Dirac quantization condition for such models involves a local system of integral symplectic spaces, giving rise to a bundle of polarized Abelian varieties equipped with a symplectic flat connection, which is defined over the scalar manifold of the theory. Generalized Einstein-Scalar-Maxwell models arise as the bosonic sector of the effective theory of string/M-theory compactifications to four-dimensions, and they are characterized by having non-trivial solutions of “U-fold” type.
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Notes
- 1.
Descriptions which are valid only if one restricts all fields to contractible open subsets of M.
- 2.
Notice however that we use different conventions.
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Acknowledgements
The authors thank Tomas Ortin for discussions and correspondence. The work of C. I. L. was supported by grant IBS-R003-S1. The work of C.S.S. was supported by the ERC Starting Grant 259133 – Observable String.
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Lazaroiu, C.I., Shahbazi, C.S. (2018). The Global Formulation of Generalized Einstein-Scalar-Maxwell Theories. In: Dobrev, V. (eds) Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 2. LT-XII/QTS-X 2017. Springer Proceedings in Mathematics & Statistics, vol 255. Springer, Singapore. https://doi.org/10.1007/978-981-13-2179-5_16
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DOI: https://doi.org/10.1007/978-981-13-2179-5_16
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