Electromagnetic fluxes, monopoles, and the order of the 4d compact U(1) phase transition

TL;DR

This paper investigates the phase transition in 4d compact U(1) gauge theory with an extended action, demonstrating it is first-order and analyzing the role of electromagnetic fluxes and monopoles.

Contribution

It provides a full phase diagram characterization using flux, relates the helicity modulus as an order parameter, and challenges the universality of the renormalized coupling at the transition.

Findings

Transition is first-order based on finite-size analysis of the helicity modulus.

The helicity modulus serves as an effective order parameter.

Counterexample to the conjectured universal value of the renormalized coupling.

Abstract

We consider the 4d compact U(1) gauge theory with extended action S=-beta sum_P cos theta_P -gamma sum_P cos 2 theta_P We give a full characterization of the phase diagram of this model using the notion of flux. The relation with the usual monopole picture is discussed. In analogy with the XY model we consider the helicity modulus \cite{Jose:1977gm} for this theory, and show that it is an order parameter. Analyzing the finite-size effects of the helicity modulus we conclude that the transition is first-order. The value of this order parameter is related to the renormalized coupling beta_R. We measure beta^c_R at the transition point and give a counterexample to its conjectured universal value \cite{Cardy:jg}.