BSM

Abstract

We review recent progress concerning the mathematical problem of determining existence, uniqueness, and structure of zero-energy states in supermembrane matrix models, relevant for the quantum mechanical description of relativistic membranes, reduced Yang-Mills theory, and M-theory. Different approaches to this problem involve octonionic deformations, averaging of simpler subsystems, as well as a well-defined Witten index counting the number of weakly decaying zero-energy states.