Abstract

In this note we summarize some of the results found recently in [1]. We show the pure discreteness of the nonperturbative quantum spectrum of a symplectic Yang-Mills theory defined on a Riemann surface of positive genus, living in a target space that, in particular, can be 4D. This theory corresponds to the membrane with central charges. The presence of the central charge induces a confinement in the phase at zero temperature. When the energy rises, the center of the group breaks and the theory enters in a quark-plasma phase after a topological transition, corresponding to the N = 4 wrapped supermembrane. (C) 2007 WILEY-VCH Verlag GmbH Co. KGaA, Weinheim.