Spectra of supersymmetric Yang-Mills quantum mechanics

TL;DR

This paper introduces a novel computational method for solving supersymmetric quantum mechanics problems by implementing a finite cut-off Hilbert space, enabling automatic numerical solutions and confirming previous results while deriving new insights, especially for D=4 systems.

Contribution

A new algebraic method for solving supersymmetric quantum mechanics problems with finite cut-off Hilbert spaces, applicable to D=2 and D=4 systems, with potential extension to D=10.

Findings

Convergence observed with increasing cut-off in multiple cases

Confirmed many existing results in supersymmetric quantum mechanics

Derived new results for D=4 supersymmetric Yang-Mills quantum mechanics

Abstract

The new method of solving quantum mechanical problems is proposed. The finite, i.e. cut off, Hilbert space is algebraically implemented in the computer code with states represented by lists of variable length. Complete numerical solution of a given system is then automatically obtained. The technique is applied to Wess-Zumino quantum mechanics and D=2 and D=4 supersymmetric Yang-Mills quantum mechanics with SU(2) gauge group. Convergence with increasing cut-off was observed in many cases, well within the reach of present machines. Many old results were confirmed and some new ones, especially for the D=4 system, are derived. Extension to D=10 is possible but computationally demanding for higher gauge groups.