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

Garcia del Moral, Maria Pilar (Departamento de Física, Universidad de Antofagasta, Aptdo 02800, Chile) ; Pena, J. M. (Departamento de Física, Facultad de Ciencias, Universidad Central de Venezuela, Apartado Postal 47270, Caracas 1041-A, Venezuela) ; Restuccia, Alvaro (Departamento de Física, Universidad de Antofagasta, Aptdo 02800, Chile)

10 July 2019

Abstract: We obtain the complete classification of the inequivalent classes of M2-brane symplectic torus bundles with monodromy in $SL\left(2,Z\right)$ and the precise $U$-duality relations among them. There are eight inequivalent classes of bundles whose monodromy groups, at low energies, are in correspondence with the gauging groups of the eight type II gauged supergravities in nine dimensions. Four of those have previously been found, and they correspond to the “type IIB side.” We provide the explicit realization of the remaining four classes associated with the “type IIA side.” The precise M2-brane $U$-duality relations between the eight inequivalent classes of bundles have allowed us to identify the remaining four. We conjecture that the classes of gaugings—classifying the eight types of II gauged supergravity in nine dimensions—are determined by the inequivalent coinvariant classes associated with the base and the fiber of the supermembrane bundles and their duals.

Published in: Physical Review D 100 (2019)