Supersymmetric Yang-Mills quantum mechanics

TL;DR

This paper introduces a novel algebraic computational method for solving supersymmetric Yang-Mills quantum mechanics, enabling automatic numerical solutions and confirming known results while deriving new insights, especially in higher dimensions.

Contribution

The paper presents a new algebraic approach to quantum mechanics problems, allowing automatic numerical solutions and extending analysis to higher-dimensional supersymmetric systems.

Findings

Confirmed existing results for D=2 and D=4 systems

Derived new results for D=4 supersymmetric Yang-Mills

Obtained spectrum of zero-volume glueballs in D=5 to D=10 for the first time

Abstract

The new approach to quantum mechanical problems is proposed. Quantum states are represented in an algebraic program, by lists of variable length, while operators are well defined functions on these lists. Complete numerical solution of a given system can then be automatically obtained. The method is applied to Wess-Zumino quantum mechanics and D=2 and D=4 supersymmetric Yang-Mills quantum mechanics with the SU(2) gauge group. Convergence with increasing size of the basis was observed in various cases. Many old results were confirmed and some new ones, especially for the D=4 system, are derived. Preliminary results in higher dimensions are also presented. In particular the spectrum of the zero-volume glueballs in $ 4 < D < 11 $ is obtained for the first time.