Complementarity and Stability Conditions

TL;DR

This paper investigates the relationship between the confining and Higgs phases in gauge theories, proposing that differences in heavy particle stability can indicate true phase distinctions rather than mere complementarity.

Contribution

It introduces the concept of stability conditions based on heavy particle structures to distinguish genuinely different phases in gauge theories.

Findings

Heavy particle stability differences signal phase transitions

Complementarity may not hold when heavy particle structures differ

Stability conditions serve as physical checks for phase distinctions

Abstract

We discuss the issue of complementarity between the confining phase and the Higgs phase for gauge theories in which there are no light particles below the scale of confinement or spontaneous symmetry breaking. We show with a number of examples that even though the low energy effective theories are the same (and trivial), discontinuous changes in the structure of heavy stable particles can signal a phase transition and thus we can sometimes argue that two phases which have different structures of heavy particles cannot be continuously connected and thus the phases cannot be complementary. We discuss what this means and suggest that such "stability conditions" can be a useful physical check for complementarity.