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

TL;DR

This work investigates whether the high-temperature deconfined phase of $SU(2)$ Yang–Mills theory and the finite-temperature Higgs phase in the adjoint-Higgs model form a single thermodynamic phase. Using global and higher-form symmetry analyses, a center-destabilizing deformation to a 3D adjoint Higgs model, and Hybrid Monte Carlo simulations on $16^3\times8$ and $12^3\times6$ lattices, the authors present a consistent picture in which the Higgs and deconfined regimes can be continuously connected, while the confined phase remains distinct. The findings hinge on symmetry realization patterns, emergent $U(1)^{[1]}$ 1-form symmetries in the deep Higgs limit, and numerical evidence that the temporal center structure does not distinguish the two deconfined phases when the Polyakov loop is destabilized. If confirmed with larger-volume studies and finite-size scaling, this deconfinement–Higgs continuity could refine our understanding of phase structure in non-Abelian gauge theories and inform cosmological/GUT-related phenomena where adjoint matter and monopole dynamics play roles.

Abstract

We study the finite-temperature phase structure of the four-dimensional ${\rm SU(2)}$ 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.

Figures (26)

• Figure 1: Naive phase diagram in the $(m^2, T)$ plane.
• Figure 2: Our proposed phase diagram in the $(m^2, T)$ plane.
• Figure 3: Global symmetry in $m^2\gg \Lambda_0^2$ region.
• Figure 4: Global symmetry on $T=0$ line.
• Figure 5: Global symmetry in $T\neq 0$ region.