On the Spectrum of D=2 Supersymmetric Yang-Mills Quantum Mechanics

TL;DR

This paper analyzes the spectrum of D=2 SU(N) supersymmetric Yang-Mills quantum mechanics, computing its thermal partition function and providing evidence for the spectrum's structure and the uniqueness of the Claudson-Halpern-Samuel solution.

Contribution

It offers the first detailed analysis of the spectrum structure and confirms the Claudson-Halpern-Samuel solution's uniqueness in N=3 and N=4 cases.

Findings

Computed the thermal partition function of the model

Provided evidence for the spectrum's structure

Confirmed the uniqueness of the Claudson-Halpern-Samuel solution in specific cases

Abstract

We investigate the structure of the spectrum of states in D=2 SU(N) supersymmetric Yang-Mills matrix quantum mechanics, which is a simplified model of Matrix theory. We compute the thermal partition function of this system and give evidence for the correctness of naively conjectured structure of the spectrum. It also suggests that Claudson-Halpern-Samuel solution is the unique eigenfunction of simultaneously diagonalizable hermitian operators, and we show that it is true in N=3 and N=4 cases.