The low energy dynamics of charge two dyonic instantons

TL;DR

This paper investigates the low energy behavior of charge two instantons and dyonic instantons in 5D SU(2) Yang-Mills theory, calculating the moduli space metric, potential, and analyzing their scattering and geodesic properties.

Contribution

It provides the first detailed calculation of the moduli space metric and potential for charge two instantons and dyonic instantons, including analytic and numerical analysis of their dynamics.

Findings

Instantons undergo right angled scattering after head-on collisions.

The moduli space structure and topology are elucidated using the ADHM construction.

Examples of finite-time singularities in geodesic flow are presented.

Abstract

We explore the low energy dynamics of charge two instantons and dyonic instantons in SU(2) 5-dimensional Yang-Mills. We make use of the moduli space approximation and first calculate the moduli space metric for two instantons. For dyonic instantons the effective action of the moduli space approximation also includes a potential term which we calculate. Using the ADHM construction we are able to understand some aspects of the topology and structure of the moduli space. We find that instantons undergo right angled scattering after a head on collision and we are able to give an analytic description of this in terms of a quotient of the moduli space by symmetries of the ADHM data. We also explore the scattering of instantons and dyonic instantons numerically in a constrained region of the moduli space. Finally we exhibit some examples of closed geodesics on the moduli space, and geodesics which hit the moduli space singularities in finite time.