Magnetic monopoles in U(1)_4 Lattice Gauge Theory with Wilson action

TL;DR

This paper constructs Green functions for magnetic monopoles in a U(1)_4 lattice gauge theory, revealing monopole condensation in strong coupling and sector splitting in the QED phase, advancing understanding of topological excitations.

Contribution

It introduces a method to construct monopole Green functions and analyzes their behavior across different coupling regimes in lattice gauge theory.

Findings

Monopole condensation occurs in the strong coupling regime.

The physical Hilbert space splits into sectors labeled by magnetic charge.

The study provides insights into topological excitations in lattice gauge theories.

Abstract

We construct the Euclidean Green functions for the soliton (magnetic monopole) field in the U(1)_4 Lattice Gauge Theory with Wilson action. We show that in the strong coupling regime there is monopole condensation while in the QED phase the physical Hilbert space splits into orthogonal soliton sectors labelled by integer magnetic charge.