(S)QCD on R^3 x S^1: Screening of Polyakov loop by fundamental quarks and the demise of semi-classics

TL;DR

This paper investigates how fundamental quarks influence the confinement-deconfinement transition and the stability of center symmetry in gauge theories on R^3 x S^1, revealing the limitations of semiclassical methods in the presence of light quarks.

Contribution

It demonstrates that quarks deform instanton-monopoles through quantum fluctuations, invalidating the semiclassical molecular picture and indicating the need for a dual description at small quark masses.

Findings

Polyakov loop exhibits a crossover from center-symmetric to broken phase with increasing 1/L.

Quarks do not contribute to monopole binding in the semiclassical regime.

Semiclassical approximation fails as quarks mediate long-range forces at small quark masses.

Abstract

Recently, it was argued that the thermal deconfinement transition in pure Yang-Mills theory is continuously connected to a quantum phase transition in softly-broken N=1 SYM theory on R^3 x S^1. The transition is semiclassically calculable at small S^1 size L, occurs as the soft mass m_soft and L vary, and is driven by a competition between perturbative effects and nonperturbative topological molecules. These are correlated instanton--anti-instanton tunneling events, whose constituents are monopole-instantons "bound" by attractive long-range forces. The mechanism driving the transition is universal for all simple gauge groups, with or without a center, such as SU(N) or G_2. Here, we consider theories with fundamental quarks. We examine the role topological objects play in determining the fate of the (exact or approximate) center-symmetry in SU(2) SQCD, with or without soft-breaking terms. In theories whose large-m_soft limit is thermal nonsupersymmetric QCD with massive quarks, we find a crossover of the Polyakov loop, from approximately center-symmetric at small 1/L to maximally center-broken at larger 1/L, as seen in lattice thermal QCD with massive quarks and T=1/L. We argue that in all calculable cases, including SQCD with exact center symmetry, quarks deform instanton-monopoles by their quantum fluctuations and do not contribute to their binding. The semiclassical approximation and the molecular picture of the vacuum fail, upon decreasing the quark mass, precisely when quarks would begin mediating a long-range attractive force between monopole-instantons, calling for a dual description of the resulting strong-coupling theory.