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

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.