Deconfinement-Higgs continuity in $\mathrm{SU}(2)$ adjoint Higgs model at finite temperature

Abstract

We study the finite-temperature phase structure of the four-dimensional $\mathrm{SU}(2)$ adjoint Higgs model, focusing on a possible \textit{deconfinement-Higgs continuity}: the conjecture that the high-temperature deconfined phase of Yang-Mills theory and the finite-temperature Higgs phase form a single thermodynamic phase. We first perform a global-symmetry analysis, showing that the Higgs and deconfined regimes are expected to share the same symmetry pattern, which is distinct from that of the confined phase. This suggests deconfinement-Higgs continuity, but does not exclude the possibility that the deconfined phase and the Higgs phase are separated by a phase transition not associated with the global symmetries. We then perform a deformation analysis, which yields an explicit continuous path between the ``deconfined symmetric'' and ``deconfined Higgs'' regions in a reduced three-dimensional lattice model. These results indicate that the Higgs and deconfined regimes can be continuously connected, while the confined phase remains distinct.

Comments: 35 pages, 22 figures