On Zero-Mass Bound States in Super-Membrane Models

TL;DR

This paper investigates zero-mass bound states in supermembrane models, showing that real solutions to the effective Schrödinger equation do not exist, but complex solutions are possible, highlighting the mathematical structure of these models.

Contribution

It provides a detailed analysis of symmetry reductions and the nature of solutions in supermembrane matrix models, focusing on the existence of bound states.

Findings

Real solutions are not square-integrable

Complex solutions are not excluded

Attractive delta-function potential influences bound states

Abstract

For the simplest case of a supermembrane matrix model, various symmetry reductions are given, with the fermionic contribution(s) (to an effective Schr\"odinger equation) corresponding to an attractive $\delta$-function potential (towards zero-area configurations). The differential equations are real, and are shown not to admit square-integrable real solutions (even when allowing non-vanishing boundary conditions at infinity). Complex solutions, however, are not excluded by this argument.