Thermal Ground State in Yang‐Mills Thermodynamics

We derive an a useful priori estimate for the thermal ground state of deconfining phase of SU(2) Yang‐Mills thermodynamics in four‐dimensional, flat spacetime and discuss its implications. Upon a selfconsistent spatial coarse‐graining over noninteracting, trivial‐holonomy (BPS saturated) (anti)calorons of unit topological charge modulus an inert, adjoint scalar field $|φ|$ and an effective pure‐gauge configuration $aμgs$ emerge. The modulus $|φ|>0$ defines the maximal resolution in the coarse‐grained theory and induces dynamical gauge‐symmetry breaking. Thanks to perturbative renormalizability and the fact that $|φ|$ can not absorb or emit energy‐momentum the effective action is local and simple. The temperature dependence of the effective coupling is a consequence of thermodynamical consistency and describes the Coulomb screening of a static test charge due to short‐lived monopole‐antimonopole pairs. The latter occur unresolvably as small‐holonomy excitations of (anti)calorons by the absorption of propagating fundamental gauge fields.