Sharp structure in gauge-invariant correlators
The argument
Standard practice classifies gauge-theory phases by the asymptotic behavior of gauge-invariant extended operators, from Wilson-loop area laws to order parameters for higher-form symmetries, and on that practice nonanalytic behavior of gauge-invariant correlation functions marks a physical distinction between phases. Because the phase of a vortex-line correlator linking a Wilson line changes non-analytically between Higgs and confining regimes in a 2+1D lattice gauge theory, even though on the continuity camp's own analysis no measurement on finite-energy states tracks that phase, detectability on finite-energy states cannot be a necessary condition for a physical distinction.
Does it work?
Not yet evaluated.
Premises
- 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
- 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
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 4, 2026
As a counterexample argument the inference is valid: if sharp structure in gauge-invariant correlators marks a physical distinction and such structure exists where no finite-energy measurement reaches, detectability cannot be a necessary condition. The calculational premise is solid and accepted by both camps: the vortex-line correlator phase changes non-analytically between Higgs and confining regimes. The argument therefore lives or dies on whether nonanalytic gauge-invariant correlator behavior marks a physical distinction on its own, which is the contested criterion question restated, so the argument cannot persuade the operational camp without begging it.
- Aug 3, 2026
As a counterexample argument the inference is valid: if sharp structure in gauge-invariant correlators marks a physical distinction and such structure exists where no finite-energy measurement reaches, detectability cannot be a necessary condition. The calculational premise is solid and accepted by both camps: the vortex-line correlator phase changes non-analytically between Higgs and confining regimes. The argument therefore lives or dies on whether nonanalytic gauge-invariant correlator behavior marks a physical distinction on its own, which is the contested criterion question restated, so the argument cannot persuade the operational camp without begging it.