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

TL;DR

This paper investigates the phase diagram of SU(2) Yang-Mills theory with an adjoint Weyl fermion on R^3xS^1, revealing a continuous connection between deconfinement transitions in pure Yang-Mills and supersymmetric theories through semi-classical analysis.

Contribution

It provides a semi-classical computation of the center symmetry transition in SU(2) Yang-Mills with adjoint fermions, linking deconfinement to supersymmetric limits and analyzing topological contributions.

Findings

Second order phase transition near m=0

Continuous connection between deconfinement and supersymmetric theories

Explicit calculation of nonzero-mode determinants

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.