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

We study the finite-temperature phase structure of the four-dimensional $\mathrm{S}\mathrm{U}(2)$ adjoint Higgs model, focusing on a possible 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 combine three approaches: (i) global symmetry analysis, showing that Higgs and deconfined regimes are expected to share the same symmetry pattern distinct from the confined phase; (ii) a deformation analysis, which yields an explicit continuous path between deconfined symmetric'' and deconfined Higgs’’ regions in a reduced three-dimensional lattice model; and (iii) Hybrid Monte Carlo analysis on ${16}^3\times 8$ and ${12}^3\times 6$ lattices, showing results suggestive of continuity. These results indicate that the Higgs and deconfined regimes can be continuously connected, while the confined phase remains distinct.