Duality and strong-coupling construction
The argument
Because the phase of the vortex-line correlator changes non-analytically between the regimes in a 2+1D lattice model with fundamental scalars, as shown through dualities and strong-coupling expansions, and given that nonanalytic behavior of gauge-invariant correlation functions marks a physical distinction between phases, the vortex-line phase registers a sharp difference between Higgs and confining dynamics even though the two regimes share the same symmetries. Because vortex Aharonov-Bohm phases can be measured in lattice simulations of gauge-Higgs models, the construction is also open to direct numerical test.
Does it work?
Not yet evaluated.
Premises
- SupportedThe evidence favors the claim, but the examination is incomplete or the evidence is indirect.constitution →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
- UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →Vortex Aharonov-Bohm phases can be measured as order parameters in lattice simulations of gauge-Higgs models
- InconclusiveThe evidence and argument have been examined and do not come down on either side.constitution →Nonanalytic behavior of gauge-invariant correlation functions marks a physical distinction between phases
Where it is made
Passages where sources make, criticize or mention this argument. They record where it appears, not how strong it is, and none has precedence over another.
No source is recorded as making it.
Earlier ratings
- Aug 3, 2026
The technical step is sound: granting the non-analyticity shown in the 2+1D lattice construction, the correlator phase does behave sharply differently across the two regimes, and lattice measurability makes the construction testable. But the argument's conclusion, that this sharp behavior distinguishes the regimes as physical phases, rests on the assumption that nonanalytic gauge-invariant correlators mark a physical distinction, and that criterion is itself the live dispute: the operational camp accepts the calculation while denying that it marks a distinction at all. The argument therefore stands or falls with that framework premise, which remains contested.