Supermembrane origin of type II gauged supergravities in 9D

Abstract

The M-theory origin of the IIB gauged supergravities in nine dimensions, classified according to the inequivalent classes of monodromy, is shown to exactly corresponds to the global description of the supermembrane with central charges. The global description is a realization of the sculpting mechanism of gauging (arXiv:1107.3255) and it is associated to particular deformation of fibrations. The supermembrane with central charges may be formulated in terms of sections on symplectic torus bundles with SL(2,Z) monodromy. This global formulation corresponds to the gauging of the abelian subgroups of SL(2,Z) associated to monodromies acting on the target torus. We show the existence of the trombone symmetry in the supermembrane formulated as a non-linear realization of the SL(2,Z) symmetry and construct its gauging in terms of the supermembrane formulated on an inequivalent class of symplectic torus fibration. The supermembrane also exhibits invariance under T-duality and we find the explicit T-duality transformation. It has a natural interpretation in terms of the cohomology of the base manifold and the homology of the target torus. We conjecture that this construction also holds for the IIA origin of gauged supergravities in 9D such that the supermembrane becomes the origin of all type II supergravities in 9D. The geometric structure of the symplectic torus bundle goes beyond the classification on conjugated classes of SL(2,Z). It depends on the elements of the coinvariant group associated to the monodromy group. The possible values of the (p,q) charges on a given symplectic torus bundle are restricted to the corresponding equivalence class defining the element of the coinvariant group.Comment: 41 pages, Latex. Typos corrected, references added, appendix added. Sections enlarged with more examples and clarifying explanations. Minor corrections in section 8. Results unchange

Classification of M2-brane 2-torus bundles, U -duality invariance, and type II gauged supergravities

“…At effective level, their 10D origin are the type IIB supergravity, the maximal type IIA and the two type IIA massive deformations: Romans [21] and Howe-Lambert-West (HLW) [22]. In this paper we extend the analysis of the M2-brane 'T-duality' transformation done in [20] where the four inequivalent M2-brane 2-torus bundles associated to the 'type IIB' sector were found an the other four were inferred from the 'T-duality' invariance of the Mass operator. We provide an explicit construction of the four inequivalent classes of M2-brane bundles associated to the 'type IIA side' in nine dimensions.…”

M2-branes on a constant flux background

“…with D i a covariant derivative defined in terms of the moduli of the torus, the winding numbers M i j and the harmonic one-forms. see [10]. The symplectic connection transforming under area preserving diffeomorphisms given by δ ǫ A = Dǫ.…”

“…A remarkable property of supermembrane theory is that all the five string theories at least at kinematical level and by double dimensional reduction can be obtained from it [6,7,8,9]. Recently it has been shown that M2-brane toroidally compactified is U-dual invariant [10,11].…”

T-Duality Invariance of the Supermembrane

“…In this section we introduce the T-duality transformations for the supermembrane theory [1]. This goes beyond the T-duality of superstring theory.…”

“…In particular, it was argued that many massive, gauged supergravities cannot be naturally embedded in string theory without such a framework [9], [10], [11]. In [1] we showed that the supermembrane on a torus with central charges is in fact the origin of type IIB, and IIA gauged supergravities in 9D. We showed the existence of a new Z 2 symmetry that plays the role of T-duality in the supermembrane interchanging the winding and KK charges but leaving the Hamiltonian invariant.…”