Monopole currents and Dirac sheets in U(1) lattice gauge theory

TL;DR

This paper demonstrates that the phases of 4D compact U(1) lattice gauge theory can be characterized by topological properties of Dirac sheets and monopole currents, revealing a percolation perspective of phase structure.

Contribution

It introduces a method to identify phase characteristics via topological analysis of Dirac sheets and monopole currents using simulated annealing.

Findings

Minimal Dirac sheets are obtained through simulated annealing.

Equivalence classes of sheet structures are the key physical quantities.

Intersections of sheets are not significant for phase characterization.

Abstract

We show that the phases of the 4-dimensional compact U(1) lattice gauge theory are unambiguously characterized by the topological properties of minimal Dirac sheets as well as of monopole currents lines. We obtain the minimal sheets by a simulated-annealing procedure. Our results indicate that the equivalence classes of sheet structures are the physical relevant quantities and that intersections are not important. In conclusion we get a percolation-type view of the phases which holds beyond the particular boundary conditions used.