trailNonanalytic behavior of gauge-invariant correlation functions marks a physical distinction between phases
Physical distinctions between phases must be detectable by measurements on finite-energy physical states
The phase of a vortex-line operator linking an electric Wilson line distinguishes Higgs from confining regimes
Standard diagnostic practice· for
Gauge theory phases are standardly diagnosed by the asymptotic behavior of gauge-invariant extended operators
atomic
In a 2+1D lattice gauge theory with fundamental scalars, the phase of a vortex-line correlator linking a Wilson line changes non-analytically between Higgs and confining regimes
Vortex Aharonov-Bohm phases can be measured as order parameters in lattice simulations of gauge-Higgs models
Generalized-symmetry grounding· for
Distinct realizations of generalized global symmetries correspond to distinct phases of matter
Confinement and deconfinement in pure Yang-Mills theory correspond to distinct realizations of the center one-form symmetry
Topological order corresponds to spontaneous breaking of higher-form global symmetries
Gauge theories with matter in the fundamental representation lack an exact one-form center symmetry
Higgs and confining regimes of gauge theories with fundamental matter are continuously connected without a phase transition
Operational measurability objection· against
Aharonov-Bohm phases of dressed quark quasiparticles interpolate smoothly between Higgs and confining regimes
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Nonanalytic behavior of gauge-invariant correlation functions marks a physical distinction between phases
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