Continuity, deconfinement, and (super) Yang-Mills theory

Abstract

We study the phase diagram of SU(2) Yang-Mills theory with one adjoint Weyl fermion on ${{\mathbb{R}}^3}\times {{\mathbb{S}}^1}$ as a function of the fermion mass m and the compactification scale L. This theory reduces to thermal pure gauge theory as m → ∞ 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 → ∞, 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 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 ${{\mathbb{R}}^3}\times {{\mathbb{S}}^1}$. 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.