Interacting ensemble of the instanton-dyons and the deconfinement phase transition in the SU(2) gauge theory

Abstract

Instanton-dyons, also known as instanton-monopoles or instanton-quarks, are topological constituents of the instantons at nonzero temperature and holonomy. We perform numerical simulations of the ensemble of interacting dyons for the SU(2) pure gauge theory, using standard Metropolis Monte Carlo and integration over parameter methods. We calculate the free energy as a function of the holonomy (logarithm of the Polyakov line) , the dyon densities, and the Debye mass, and find its minima as a function of those parameters. Unlike previous numerical study of such ensemble, we show that the back reaction on the holonomy potential does generate confinement, provided the density is sufficiently high (or the temperature sufficiently low). We then report various properties of the self-consistent ensembles as a function of temperature.

New Nonperturbative Methods in Quantum Field Theory: From Large-NOrbifold Equivalence to Bions and Resurgence

“…These results inspired various lattice studies, which exhibit remarkable matching to the theoretical predictions [127][128][129][130]. The semi-classically calculable realization of center-symmetry also inspired related works in the strong coupling regime, see [122,124,125], and lattice simulations [126].…”

Instanton-dyon ensembles with quarks with modified boundary conditions

“…Their mechanism has been discussed extensively since the 1970's: We will mention some historical highlights below. Our previous papers, to be referred to as I [1] and II [2] below, addressed those phenomena in a model based on a certain gauge topology model.…”

“…This observation lead to the proposal [12] of confinement being driven by this effect, and in a very specialized setting it has been shown to induce confinement [25,26], even for exponentially small dyon density. Recent works using mean field methods [27,28] and our own two papers [1,2] had shown that sufficiently dense ensemble of the dyons does generate both confinement and chiral symmetry breaking, with close transition temperatures (too close to separate inside the errors).…”

Confinement and Chiral Symmetry Breaking from an ensemble of interacting Instanton-dyons(monopoles) in SU(2) QCD

“…The case of no fermions [1] is strongly affected by the breaking of center symmetry. In terms of dyons, breaking of center symmetry is observed as the density of M and L type dyons becoming different.…”