Classical interactions of the instanton-dyons with antidyons

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.

10 pages, 12 figures

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• Confinement, Holonomy and Correlated Instanton-Dyon Ensemble I: SU(2) Yang-Mills Theory
• Light Adjoint Quarks in the Instanton-Dyon Liquid Model IV
• Confinement in non-Abelian lattice gauge theory via persistent homology
• Deconfinement Phase Transition in the $SU(3)$ Instanton-dyon Ensemble
• Lectures on nonperturbative QCD ( Nonperturbative Topological Phenomena in QCD and Related Theories)
• Dense Instanton-Dyon Liquid Model: Diagrammatics
• Confinement from Correlated Instanton-Dyon Ensemble in SU(2) Yang-Mills Theory
• Recent progress in understanding deconfinement and chiral restoration phase transitions
• Dyons near the transition temperature in $SU(3)$ lattice gluodynamics
• Instanton-dyon ensembles reproduce deconfinement and chiral restoration phase transitions
• Density and correlations of topological objects near the transition temperature in lattice gluodynamics