Absence of Zero Energy States in Reduced SU(N) 3d Supersymmetric Yang Mills Theory

TL;DR

This paper investigates a supersymmetric matrix model related to membranes in four-dimensional spacetime, demonstrating that a specific inner product involving solutions to certain supersymmetry equations vanishes, indicating the absence of zero energy states.

Contribution

It provides a proof that zero energy states do not exist in a reduced SU(N) 3d supersymmetric Yang-Mills theory, clarifying the spectral properties of the model.

Findings

Zero energy states are absent in the model.

The inner product between certain supersymmetric solutions is zero.

The result impacts understanding of supersymmetry in membrane models.

Abstract

For the SU(N) invariant supersymmetric matrix model related to membranes in 4 space-time dimensions we argue that <Psi,chi> = 0 for the previously obtained solution of Q chi = 0, Q^{dagger} Psi = 0.