Revision 1

Accepted · first revision · record

Title: Sharp distinction between Higgs and confining phases with fundamental matter
Plain: With quarks present, the usual test for confinement fails, and the confining phase and the Higgs phase (where a condensed field gives the force carriers mass) seem smoothly connected. Whether some generalized symmetry or order parameter still separates them is unknown.
Precise: With dynamical matter in the fundamental representation, the $Z_N$ one-form center symmetry is explicitly broken and the Wilson-loop area law is no longer an order parameter; Fradkin and Shenker (1979) showed the phases can be connected. Determine whether, in theories with additional global symmetries (for example a $U(1)$ broken in both regimes, as in dense QCD), a vortex-holonomy or other non-local order parameter sharply separates Higgs and confining phases, and whether this holds generally.
Settled by: A proof that the proposed order parameter is quantized and differs between the phases, confirmed by lattice simulation of a model with a phase transition along every path.
Kind: well-posed
Answer type: yes-no
References: (empty)
Literature status: contested
Status note: Cherman, Jacobson, Sen and Yaffe (2020-2024) proposed a vortex-holonomy order parameter; its validity is disputed, and lattice studies (2023-2025) report gauge-independent transitions in SU(2) gauge-scalar models.
Posed since: 1979