Supermembrane origin of type II gauged supergravities in 9D

TL;DR

This paper demonstrates that the origin of nine-dimensional type II gauged supergravities can be understood through the global description of supermembranes with central charges, revealing new symmetries and dualities in the process.

Contribution

It establishes a novel connection between supermembrane formulations and gauged supergravities in 9D, including the realization of trombone symmetry and T-duality within this framework.

Findings

Supermembrane with central charges corresponds to gauged supergravities in 9D.

Existence of trombone symmetry in supermembrane formulation.

Explicit T-duality transformation and its geometric interpretation.

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.