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

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

2009-09-16

arxiv.org/abs/0909.3064v2

Phys.Rev.Lett.104:181601,2010

Physics

High Energy Physics

High Energy Physics - Theory

4 pages, RevTeX. Some equations simplified. Version to appear in Physical Review Letters

Scientific paper

10.1103/PhysRevLett.104.181601

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 $L^3$.

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