Notes on the Dynamics of Noncommutative U(2) and Commutative SU(3) Instantons

TL;DR

This paper studies the dynamics of specific noncommutative and commutative instantons in 5d Super Yang Mills theory, constructing explicit solutions, analyzing their moduli spaces, and performing numerical simulations.

Contribution

It provides explicit construction of 1/4-BPS instanton solutions, detailed analysis of their moduli spaces, and numerical methods for simulating their dynamics.

Findings

Successful construction of instanton solutions using biquaternions

Numerical analysis of moduli space dynamics

Discussion of numerical challenges and solutions

Abstract

We examine the dynamics of noncommutative instantons of instanton number $2$ and commutative instantons of instanton number $3$ in 5d Super Yang Mills theory. We begin by detailing the construction of the 1/4-BPS instanton solutions, their moduli space, and the moduli space potential using an explicit parametrisation of the moduli space coordinates in terms of the biquaternions. We then go on to numerically analyse the dynamics on the moduli spaces we have constructed, discussing some of the numerical issues which arose and describing the code we developed to solve them