Moduli Space Dynamics of Noncommutative U(2) Instantons

TL;DR

This paper studies the low-energy behavior of charge two noncommutative U(2) instantons in 5D super-Yang-Mills, analyzing their moduli space geometry and the effects of potentials on scattering dynamics.

Contribution

It provides a detailed calculation of the moduli space metric for noncommutative instantons using the ADHM construction and explores the impact of potentials on dyonic instanton scattering.

Findings

Computed the moduli space metric for noncommutative instantons.

Analyzed the topology and geometry of the instanton moduli space.

Derived scattering results for noncommutative dyonic instantons.

Abstract

We consider the low energy dynamics of charge two instantons on noncommutative $\mathbb{R}^{2}_{NC}\times\mathbb{R}^{2}_{NC}$ in U(2) 5-dimensional super-Yang-Mills, using the Manton approximation for slow-moving instantons to calculate the moduli space metric. By employing the ADHM construction, we are able to understand some aspects of the geometry and topology of the system. We also consider the effect of adding a potential to the moduli space, giving scattering results for noncommutative dyonic instantons.