On the Construction of Zero Energy States in Supersymmetric Matrix Models

TL;DR

This paper investigates the construction of zero energy states in supersymmetric matrix models related to membranes, providing explicit solutions for certain models in 4 and 11 dimensions, advancing understanding of their quantum states.

Contribution

It explicitly determines solutions to supersymmetric equations in SU(N) models for odd N and outlines solutions in 11-dimensional models, contributing new methods for constructing zero energy states.

Findings

Explicit solutions for SU(N) models with odd N

Formal construction of fermionic states from bosonic solutions

Outline of solutions in 11-dimensional models

Abstract

For the SU(N) invariant supersymmetric matrix model related to membranes in 4 space-time dimensions, the general solution to the equation(s) $Q^{\dagger}\Psi=0$ $(Q\chi =0)$ is determined for N odd. For any such (bosonic) solution of $Q^{\dagger}\Psi=0$, a (fermionic) $\Phi$ is found that (formally) satisfies $Q^{\dagger}\Phi=\Psi$. For the analogous model in 11 dimensions the solution of $Q^{\dagger}\Psi=0 (Q\Psi=0)$ is outlined.