Continuity, Deconfinement, and (Super) Yang-Mills Theory

TL;DR

The work provides a cohesive semi-classical account linking the deconfinement transition of pure Yang–Mills to center-symmetry dynamics in softly broken ${\cal N}=1$ theories on ${\mathbb R}^3\times{\mathbb S}^1$, demonstrated through a detailed analysis of perturbative and nonperturbative effects. Central to the mechanism are topological molecules—magnetic bions that induce a dual-photon mass gap and neutral (center-stabilizing) bions whose contributions, computed via the Bogomolny–Zinn-Justin prescription, stabilize center symmetry and shape the holonomy potential. The authors show that the center-symmetry changing transition can be computed semi-classically at small $L$ and that the same physics persists in pure YM, suggesting a continuous connection to the thermal deconfinement transition with $L_c(m) o 1/T_c$ as $m\to\infty$. They also discuss non-cancellation of nonzero-mode determinants around supersymmetric monopole backgrounds, arguing its necessity for consistency with holomorphy and supersymmetry, and map monopole towers to dyon spectra via Poisson duality. These results offer a concrete analytic handle on confinement physics and provide testable predictions for lattice studies and extensions to higher gauge groups and $\theta$-dependence.

Abstract

We study the phase diagram of SU(2) Yang-Mills theory with one adjoint Weyl fermion on R^3xS^1 as a function of the fermion mass m and the compactification scale L. This theory reduces to thermal pure gauge theory as m->infinity and to circle-compactified (non-thermal) supersymmetric gluodynamics in the limit m->0. In the m-L plane, there is a line of center symmetry changing phase transitions. In the limit m->infinity, this transition takes place at L_c=1/T_c, where T_c is the critical temperature of the deconfinement transition in pure Yang-Mills theory. We show that near m=0, the critical compactification scale L_c can be computed using semi-classical methods and that the transition is of second order. This suggests that the deconfining phase transition in pure Yang-Mills theory is continuously connected to a transition that can be studied at weak coupling. The center symmetry changing phase transition arises from the competition of perturbative contributions and monopole-instantons that destabilize the center, and topological molecules (neutral bions) that stabilize the center. The contribution of molecules can be computed using supersymmetry in the limit m=0, and via the Bogomolnyi--Zinn-Justin (BZJ) prescription in the non-supersymmetric gauge theory. Finally, we also give a detailed discussion of an issue that has not received proper attention in the context of N=1 theories---the non-cancellation of nonzero-mode determinants around supersymmetric BPS and KK monopole-instanton backgrounds on R^3xS^1. We explain why the non-cancellation is required for consistency with holomorphy and supersymmetry and perform an explicit calculation of the one-loop determinant ratio.