Solution to the gauge-Higgs analyticity paradox

TL;DR

This paper resolves a paradox in gauge-Higgs theories by identifying a flaw in previous proofs, demonstrating that Higgs and confinement phases are separated by a phase boundary, and introducing a new order parameter for simulations.

Contribution

The authors identify a flaw in the Fradkin-Shenker theorem and related proofs, clarifying the phase structure in gauge-Higgs systems and proposing a new order parameter for better analysis.

Findings

The paradox in gauge-Higgs analyticity is resolved.

Higgs and confinement phases are separated by a phase boundary.

A new gauge-invariant order parameter is introduced for Monte Carlo simulations.

Abstract

The Fradkin-Shenker theorem proves analyticity in a region that connects Higgs to confinement regimes, precluding a phase transition. This conflicts with a simpler analyticity argument applicable to any symmetry-breaking phase transition that requires the phase diagram to be bifurcated. A flaw in the Fradkin-Shenker and related Osterwalder-Seiler proofs is found which removes this paradox. Higgs and Confinement regions are everywhere separated by a phase boundary. A new order parameter allowing this transition to be traced with Monte-Carlo simulations without gauge fixing is introduced.