A regulated zero-temperature construction of the Fundamental Modular Region in pure Yang--Mills theory and QCD

Abstract

We formulate the Fundamental Modular Region (FMR) as the zero-temperature limit of regulated copy-weighted Landau gauges. At finite $β$, the measure localizes on absolute minima, and the leading correction is dominated by the inverse Faddeev--Popov (FP) operator. A small $SU(2)$ benchmark provides a computational realization through population annealing and collective basin hopping. Our construction defines absolute Landau gauge without parametrizing the FMR boundary and extends naturally to full quantum chromodynamics (QCD). It also admits a Hamiltonian interpretation in terms of the gauge-fixed vacuum wave functional on the FMR.