Compact $z=2$ Electrodynamics in 2+1 dimensions: Confinement with gapless modes

TL;DR

This paper studies a 2+1 dimensional compact U(1) gauge theory at a Lifshitz point with z=2, revealing confinement of minimal charges and a unique behavior of spacelike Wilson loops due to monopole effects.

Contribution

It introduces a non-relativistic Sine-Gordon model for monopoles at z=2, showing the persistence of a gapless mode and novel confinement properties distinct from z=1 theories.

Findings

Monopoles induce confinement of minimal charges via timelike Wilson loops.

Spacelike Wilson loops scale as L^3, indicating a different confinement behavior.

A gapless mode remains due to shift invariance, despite monopole proliferation.

Abstract

We consider 2+1 dimensional compact U(1) gauge theory at the Lifshitz point with dynamical critical exponent $z=2$. As in the usual $z=1$ theory, monopoles proliferate the vacuum for any value of the coupling, generating a mass scale. The theory of the dilute monopole gas is written in terms a non-relativistic Sine-Gordon model with two real fields. While monopoles remove some of the massless poles of the perturbative field strength propagator, a gapless mode representing the incomplete screening of monopoles remains, and is protected by a shift invariance of the original theory. Timelike Wilson loops still obey area laws, implying that minimal charges are confined, but the action of spacelike Wilson loops of linear size L goes instead as $L^3$.