Phase Diagram of Compact U(1) gauge theory – a Renormalization Group approach

It was shown by Polyakov that Maxwell theory in 3+1 dimensions can go through a deconfinement – confinement phase transition if the U(1) gauge field is compact. This happens due to a non-perturbative mechanism where monopoles proliferate when the Maxwell coupling exceeds a critical value. In this work, we revisit this phase transition using a renormalization group (RG) approach. The key players in our approach are fields defined on closed strings as opposed to points. We highlight curious aspects of this RG on closed strings that have no analog in conventional field theory. We then explore the phase diagram as a function of the Maxwell coupling and temperature.