(S)QCD on ${{\mathbb{R}}^3}\times {{\mathbb{S}}^1}$: screening of Polyakov loop by fundamental quarks and the demise of semi-classics

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 $\mathcal{N}=1$ supersymmetric pure YM theory on ${{\mathbb{R}}^3}\times {{\mathbb{S}}^1}$. The transition is semiclassically calculable at small ${{\mathbb{S}}^1}$ 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-antiinstanton 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 _c ) 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) supersymmetric QCD (SQCD) with fundamental flavors, 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 $\frac{1}{L}$ to maximally center-broken at larger $\frac{1}{L}$ , as seen in lattice thermal QCD with massive dynamical quarks and $T=\frac{1}{L}$. 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.