Fluxes, twisted tori, monodromy and U(1) supermembranes
Abstract We show that the D = 11 supermembrane theory (M2-brane) compactified on a M 9 × 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 fibere...
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doaj-867a45a80d6a4e3ca09e8eb344c4625f2020-11-25T03:24:00ZengSpringerOpenJournal of High Energy Physics1029-84792020-09-012020912710.1007/JHEP09(2020)097Fluxes, twisted tori, monodromy and U(1) supermembranesM. P. Garcia del Moral0C. Las Heras1P. Leon2J. M. Pena3A. Restuccia4Departamento de Física, Universidad de AntofagastaDepartamento de Física, Universidad de AntofagastaDepartamento de Física, Universidad de AntofagastaDepartamento de Física, Universidad de AntofagastaDepartamento de Física, Universidad de AntofagastaAbstract We show that the D = 11 supermembrane theory (M2-brane) compactified on a M 9 × 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 π 0(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.http://link.springer.com/article/10.1007/JHEP09(2020)097M-TheoryFlux compactificationsGauge Symmetry |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
M. P. Garcia del Moral C. Las Heras P. Leon J. M. Pena A. Restuccia |
spellingShingle |
M. P. Garcia del Moral C. Las Heras P. Leon J. M. Pena A. Restuccia Fluxes, twisted tori, monodromy and U(1) supermembranes Journal of High Energy Physics M-Theory Flux compactifications Gauge Symmetry |
author_facet |
M. P. Garcia del Moral C. Las Heras P. Leon J. M. Pena A. Restuccia |
author_sort |
M. P. Garcia del Moral |
title |
Fluxes, twisted tori, monodromy and U(1) supermembranes |
title_short |
Fluxes, twisted tori, monodromy and U(1) supermembranes |
title_full |
Fluxes, twisted tori, monodromy and U(1) supermembranes |
title_fullStr |
Fluxes, twisted tori, monodromy and U(1) supermembranes |
title_full_unstemmed |
Fluxes, twisted tori, monodromy and U(1) supermembranes |
title_sort |
fluxes, twisted tori, monodromy and u(1) supermembranes |
publisher |
SpringerOpen |
series |
Journal of High Energy Physics |
issn |
1029-8479 |
publishDate |
2020-09-01 |
description |
Abstract We show that the D = 11 supermembrane theory (M2-brane) compactified on a M 9 × 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 π 0(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. |
topic |
M-Theory Flux compactifications Gauge Symmetry |
url |
http://link.springer.com/article/10.1007/JHEP09(2020)097 |
work_keys_str_mv |
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