One-Loop Free Energy of the Four-Dimensional Compact QED in the Confining Phase

TL;DR

This paper calculates the one-loop free energy of four-dimensional compact QED in the confining phase, revealing different decay behaviors depending on the strength tensor's norm and monopole loop configurations.

Contribution

It provides an explicit calculation of the free energy in strong coupling regimes, linking the results to the vector Sine-Gordon model and monopole loop configurations.

Findings

Free energy decays exponentially with the norm of the strength tensor in certain regimes.

In the zero configuration case, free energy decays with the inverse square of loop area.

Different decay behaviors are identified depending on the dominant Sine-Gordon configuration.

Abstract

The one-loop free energy of the four-dimensional compact QED, which is known to be equivalent to the vector Sine-Gordon model, is calculated in the strong coupling regime. In the case, when the norm of the strength tensor of the saddle-point value of the corresponding Sine-Gordon model is much larger than the typical inverse area of a loop in the gas of the monopole rings, the obtained free energy decays exponentially versus this norm. In the opposite case, when the dominant configuration of the Sine-Gordon model is identically zero, the resulting free energy decays with the growth of loops as an exponent of the inverse square of their typical area.