Classical interactions of the instanton-dyons with antidyons

TL;DR

This paper investigates the classical interactions between instanton-dyons and antidyons by solving the gradient flow equations on a lattice, revealing a unique streamline behavior ending in a quasi-stationary state.

Contribution

It provides the first classical analysis of dyon-antidyon interactions, including parametrization of streamline configurations for future many-body studies.

Findings

Streamline configurations are largely independent of initial conditions.

The interaction flow ends at a quasi-stationary configuration.

The action of these configurations is parametrized for future use.

Abstract

Instanton-dyons, also known as instanton-monopoles or instanton-quarks, are topological constituents of the instantons at nonzero temperature and nonzero expectation value of $A_4$. While the interaction between instanton-dyons has been calculated to one-loop order by a number of authors, that for dyon-antidyon pairs remains unknown even at the classical level. In this work we are filling this gap, by solving the gradient flow equation on a 3d lattice. We start with two well separated objects. We find that, after initial rapid relaxation, the configurations follow "streamline" set of configurations, which is basically independent on the initial configurations used. In striking difference to instanton-antiinstanton streamlines, in this case it ends at a quasi-stationary configuration, with an abrupt drop to perturbative fields. We parameterize the action of the streamline configurations, which is to be used in future many-body calculations.