Fluxes, twisted tori, monodromy and U(1) supermembranes
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Springer
Received: June 1, 2020 Accepted: August 13, 2020 Published: September 15, 2020
M.P. Garcia del Moral, C. Las Heras, P. Leon, J.M. Pena and A. Restuccia Departamento de F´ısica, Universidad de Antofagasta, Avda. Universidad de Antofagasta 02800, Antofagasta, Chile
E-mail: [email protected], [email protected], [email protected], [email protected], [email protected] Abstract: We show that the D = 11 supermembrane theory (M2-brane) compactified on a M9 × T 2 target space, with constant fluxes C± naturally incorporates the geometrical structure of a twisted torus. We extend the M2-brane theory to a formulation on a twisted torus bundle. It is consistently fibered over the world volume of the M2-brane. It can also be interpreted as a torus bundle with a nontrivial U(1) connection associated to the fluxes. The structure group G is the area preserving diffeomorphisms. The torus bundle is defined in terms of the monodromy associated to the isotopy classes of symplectomorphisms with π0 (G) = SL(2, Z), and classified by the coinvariants of the subgroups of SL(2, Z). The spectrum of the theory is purely discrete since the constant flux induces a central charge on the supersymmetric algebra and a modification on the Hamiltonian which renders the spectrum discrete with finite multiplicity. The theory is invariant under symplectomorphisms connected and non connected to the identity, a result relevant to guarantee the U-dual invariance of the theory. The Hamiltonian of the theory exhibits interesting new U(1) gauge and global symmetries on the worldvolume induced by the symplectomorphim transformations. We construct explicitly the supersymmetric algebra with nontrivial central charges. We show that the zero modes decouple from the nonzero ones. The nonzero mode algebra corresponds to a massive superalgebra that preserves either 1/2 or 1/4 of the original supersymmetry depending on the state considered. Keywords: M-Theory, Flux compactifications, Gauge Symmetry ArXiv ePrint: 2005.06397v1
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP09(2020)097
JHEP09(2020)097
Fluxes, twisted tori, monodromy and U(1) supermembranes
Contents 1 Introduction
1
2 M2-brane with constant C± fluxes
4
3 Supercharges algebra of the M2-brane with constant C± fluxes
6 9 10 11
5 Symmetries of the M2-brane theory with fluxes 5.1 Hamiltonian symmetries
14 18
6 Geometrical interpretation: a M2-brane on a twisted torus bundle 6.1 Twisted 3-torus 6.2 The supermembrane on a twisted torus bundle
19 20 21
7 Discussion and conclusions
22
1
Introduction
Flux compactifications have provided a new arena to explore String theory realizations with very good results towards the recovering of phenomenological properties at low energies. They are topological quantities associated to the quantization condition of closed field strength p-forms over compact p-cycles. They may modify the string theory compactifications in many ways, for example in the amount of supersymmetry preserved, by
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