Analytical approach to SU(2) Yang-Mills thermodynamics

Abstract

We propose an analytical approach to SU(2) Yang-Mills thermodynamics. The existence of a macroscopic and rigid adjoint Higgs field, generated by dilute trivial-holonomy calorons at large temperature $T$ (electric phase), implies a twofold degeneracy of the ground state which signals a broken electric $Z_2$ symmetry. A finite energy density $\propto T$ of the ground state arises due to caloron interaction. An evolution equation for the effective gauge coupling, derived from thermodynamical self-consistency, predicts a second-order like transition (seen in lattice simulations) at $T_c$ to a phase where monopoles are condensed and off-Cartan excitations decoupled. In this magnetic phase the ground state is unique and dominates the pressure (negative total pressure). While the magnetic phase has a massive, propagating 'photon' it confines fundamental matter (pre-confinement). The temperature dependence of the magnetic gauge coupling predicts the transition to the confining phase at $T_C\sim \frac{T_c}{1.9}$ where center-vortex loops condense and the 'photon' decouples. We believe that this transition is 'swallowed' by finite-size artefacts in lattice simulations. No thermodynamical connection exists between the confining and the magnetic phase.