Topological Excitations in Compact Maxwell-Chern-Simons Theory

TL;DR

This paper develops a lattice model for (2+1)-dimensional Maxwell-Chern-Simons theory, identifying topological excitations as monopole-antimonopole pairs connected by observable, finite-energy strings that exhibit confinement and topological linking interactions.

Contribution

It introduces a lattice formulation of the theory, characterizes the topological excitations, and reveals their interactions, including confinement and linking effects.

Findings

Topological excitations are monopole-antimonopole pairs connected by observable strings.

Strings carry both magnetic flux and electric charge, leading to confinement.

Strings interact via a topological linking term.

Abstract

We construct a lattice model of compact (2+1)-dimensional Maxwell-Chern- Simons theory, starting from its formulation in terms of gauge invariant quantities proposed by Deser and Jackiw. We thereby identify the topological excitations and their interactions. These consist of monopolo- antimonopole pairs bounded by strings carrying both magnetic flux and electric charge. The electric charge renders the Dirac strings observable and endows them with a finite energy per unit length, which results in a linearly confining string tension. Additionally, the strings interact via an imaginary, topological term measuring the (self-) linking number of closed strings.