Solutions of Extended Supersymmetric Matrix Models for Arbitrary Gauge Groups

TL;DR

This paper finds energy eigenstates for N=2 supersymmetric gauged quantum mechanics with SU(n) and U(n) gauge groups, revealing a continuous spectrum and providing perturbative solutions for N>2 relevant to M theory.

Contribution

It provides explicit solutions for N=2 supersymmetric matrix models with arbitrary gauge groups and extends to perturbative solutions for N>2, connecting to M theory.

Findings

Energy eigenstates for N=2 models with SU(n) and U(n)

Spectrum is continuous for these models

Perturbative eigenstates for N>2 are derived

Abstract

Energy eigenstates for N=2 supersymmetric gauged quantum mechanics are found for the gauges groups SU(n) and U(n). The analysis is aided by the existence of an infinite number of conserved operators. The spectum is continuous. Perturbative eigenstates for $N>2$ are also presented, a case which is relevant for the conjectured description of M theory in the infinite momentum frame.