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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Main Authors: M. P. Garcia del Moral, C. Las Heras, P. Leon, J. M. Pena, A. Restuccia
Format: Article
Language:English
Published: SpringerOpen 2020-09-01
Series:Journal of High Energy Physics
Subjects:
Online Access:http://link.springer.com/article/10.1007/JHEP09(2020)097
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spelling 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
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