Magnetic Symmetries and Vortices In Chern-Simons Theories

TL;DR

This paper investigates the properties of vortex operators in 2+1 dimensional Chern-Simons theories, revealing their local nature, UV divergence issues, and potential for magnetic symmetry breaking and confinement at small Chern-Simons levels.

Contribution

It demonstrates the existence of local vortex operators in these theories and explores their behavior and implications for magnetic symmetry and confinement.

Findings

Vortex operators are local in UV regularized theories.

Vortex energy diverges logarithmically in the continuum limit.

Small Chern-Simons coefficient may lead to vortex condensation and confinement.

Abstract

We study the locality properties of the vortex operators in compact U(1) Maxwell-Chern-Simons and SU(N) Yang-Mills-Chern-Simons theories in 2+1 dimensions. We find that these theories do admit local vortex operators and thus in the UV regularized versions should contain stable magnetic vortices. In the continuum limit however the energy of these vortex excitations generically is logarithmically UV divergent. Nevertheless the classical analysis shows that at small values of CS coefficient $\kappa$ the vortices become light. It is conceivable that they in fact become massless and condense due to quantum effects below some small $\kappa$. If this happens the magnetic symmetry breaks spontaneously and the theory is confining.