On the Higgs-Confinement Complementarity

TL;DR

This paper clarifies that Higgs-confinement complementarity is consistent and not paradoxical, reaffirming the mathematical and physical validity of the concept in gauge theories.

Contribution

It provides a detailed analysis confirming the absence of paradoxes and mathematical flaws in the Higgs-confinement complementarity argument.

Findings

No paradox exists in Higgs-confinement transition

Mathematical reasoning supporting complementarity is sound

Higgs and confinement regimes are smoothly connected

Abstract

It has been noticed long ago that in Higgs models with `complete symmetry breaking' one can move from the confinement to the Higgs regime without crossing a phase boundary, a fact sometimes called referred to as `complementarity'. In a recent paper some doubt was raised about the correctness of the mathematics underlying this fact and it was claimed that the supposed `flaw' would resolve the `paradox' seen in this complementarity. Here we briefly revisit the facts both from a mathematical and a physical point of view and point out that (a) there is no paradox and (b) there is no flaw in the mathematical reasoning.