Update on the quantum properties of the Supermembrane

TL;DR

This paper reviews the quantum spectral properties of the supermembrane, highlighting a topological sector with a discrete spectrum and discussing implications for M2-brane theories and G2 compactifications.

Contribution

It provides a summary of quantum properties of the supermembrane, emphasizing a topological sector with discrete spectrum and its realization in various backgrounds, including G2 compactifications.

Findings

Topological sector of supermembrane has a purely discrete spectrum.

Construction implemented in toroidal and G2 orbifold backgrounds.

Comments on quantum properties of multiple M2-brane theories.

Abstract

In this note we summarize some of the quantum properties found since the early 80's until nowdays that characterize at quantum level the spectrum of the supermembrane. In particular we will focus on a topological sector of the 11D supermembrane that, contrary to the general case, has a purely discrete spectrum at supersymmetric level. This construction has been consistently implemented in different types of backgrounds: toroidal and orbifold-type with G2 structure able to lead to a true G2 compactification manifold. This theory has N=1 supersymmetries in 4D. comment on the relevant points of this construction as well as on its spectral characteristics. We will also make some comments on the quantum properties of some effective formulation of multiple M2's theories recently found.