The Supermembrane with Central Charges on a G2 Manifold

TL;DR

This paper constructs an 11D supermembrane with topological central charges on a G2 manifold, demonstrating a discrete spectrum and resulting in a 4D N=1 supersymmetric effective theory.

Contribution

It introduces a novel supermembrane model on a G2 manifold with preserved spectrum discreteness and supersymmetry, using orbifold constructions and automorphism groups.

Findings

Supermembrane spectrum remains discrete on G2 manifold.

Constructed supermembrane model with topological central charges.

Resulting 4D theory has N=1 supersymmetry.

Abstract

We construct the 11D supermembrane with topological central charges induced through an irreducible winding on a G2 manifold realized from the T7/Z2xZ2xZ2 orbifold construction. The hamiltonian H of the theory on a T7 target has a discrete spectrum. Within the discrete symmetries of H associated to large diffeomorphisms, the Z2xZ2xZ2 group of automorphisms of the quaternionic subspaces preserving the octonionic structure is relevant. By performing the corresponding identification on the target space, the supermembrane may be formulated on a G2 manifold, preserving the discretness of its supersymmetric spectrum. The corresponding 4D low energy effective field theory has N=1 supersymmetry.