On the Construction of Zero Energy States in Supersymmetric Matrix 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) $Q^{\dagger}Ψ=0$ $(Qχ=0)$ is determined for N odd. For any such (bosonic) solution of $Q^{\dagger}Ψ=0$, a (fermionic) $Φ$ is found that (formally) satisfies $Q^{\dagger}Φ=Ψ$. For the analogous model in 11 dimensions the solution of $Q^{\dagger}Ψ=0 (QΨ=0)$ is outlined.