The supermembrane with central charges:(2+1)-D NCSYM, confinement and phase transition

TL;DR

This paper demonstrates that the supermembrane with central charges has a discrete spectrum with a mass gap, indicating confinement and phase transitions analogous to quark-gluon plasma in a 2+1D non-commutative super-Yang-Mills framework.

Contribution

It extends previous results to show the spectrum's discreteness for the full supermembrane with central charges and explores its phase structure related to confinement and deconfinement.

Findings

Spectrum of the supermembrane with central charges is discrete with a mass gap.

The theory exhibits confinement and phase transitions similar to quark-gluon plasma.

Spontaneous symmetry breaking leads to different phases in the model.

Abstract

The spectrum of the bosonic sector of the D=11 supermembrane with central charges is shown to be discrete and with finite multiplicities, hence containing a mass gap. The result extends to the exact theory our previous proof of the similar property for the SU(N) regularised model and strongly suggest discreteness of the spectrum for the complete Hamiltonian of the supermembrane with central charges. This theory is a quantum equivalent to a symplectic non-commutative super-Yang-Mills in 2+1 dimensions, where the space-like sector is a Riemann surface of positive genus. In this context, it is argued how the theory in 4D exhibits confinement in the N=1 supermembrane with central charges phase and how the theory enters in the quark-gluon plasma phase through the spontaneous breaking of the centre. This phase is interpreted in terms of the compactified supermembrane without central charges.