The helicity modulus in gauge field theories

TL;DR

This paper investigates the helicity modulus as an order parameter for phase transitions in 4d compact U(1) gauge theories and extends its application to SU(2) Yang-Mills theories, offering new insights into confinement phenomena.

Contribution

It introduces the helicity modulus as a novel order parameter for phase transitions in gauge theories and extends its use to non-Abelian SU(2) theories.

Findings

Helicity modulus effectively characterizes the confinement-deconfinement transition in U(1) gauge theory.

The extended definition of the helicity modulus provides insights into SU(2) gauge theory behavior.

Flux-based characterization offers an alternative to monopole-based descriptions.

Abstract

We consider the 4d compact U(1) theory with Wilson action and characterize its phase diagram using the notion of electromagnetic flux, instead of the more usual magnetic monopole. Taking inspiration from the flux picture, we consider the helicity modulus (h.m.) for this theory, and show that it is an order parameter for the confinement deconfinement phase transition. We extend the definition of the h.m. to an Abelian projected Yang-Mills theory, and discuss its behavior in SU(2).