Self Duality and Oblique Confinement in Planar Gauge Theories

TL;DR

This paper studies two lattice gauge models with Chern-Simons interactions, revealing their phase structures and connections to condensed matter phenomena like Josephson junctions and quantum Hall effects.

Contribution

It introduces a detailed analysis of non-perturbative effects in $Z_p imes Z_p$ gauge models with Chern-Simons terms, linking topological excitations to phase transitions.

Findings

Match with quantum phase transitions in Josephson junction arrays

Identification of oblique confining states related to quantum Hall regimes

Topological excitations determine the phase structure

Abstract

We investigate the non-perturbative structure of two planar $Z_p \times Z_p$ lattice gauge models and discuss their relevance to two-dimensional condensed matter systems and Josephson junction arrays. Both models involve two compact U(1) gauge fields with Chern-Simons interactions, which break the symmetry down to $Z_p \times Z_p$. By identifying the relevant topological excitations (instantons) and their interactions we determine the phase structure of the models. Our results match observed quantum phase transitions in Josephson junction arrays and suggest also the possibility of {\it oblique confining ground states} corresponding to quantum Hall regimes for either charges or vortices.