Vortex solutions of the Lifshitz-Chern-Simons theory

TL;DR

This paper investigates vortex solutions in the Lifshitz-Chern-Simons theory, revealing their properties, energy divergence, and potential phase transition, with solutions analyzed on different geometries including hyperbolic plane and sphere.

Contribution

It provides the first analysis of vortex solutions in Lifshitz-Chern-Simons theory, including their energy behavior and effects of different spatial geometries.

Findings

Vortex solutions exist with logarithmically divergent energy.

Finite energy vortex solutions are found on the hyperbolic plane.

Vortex solutions on the sphere are also explored.

Abstract

We study vortex-like solutions to the Lifshitz-Chern-Simons theory. We find that such solutions exists and have a logarithmically divergent energy, which suggests that a Kostelitz-Thouless transition may occur, in which voxtex-antivortex pairs are created above a critical temperature. Following a suggestion made by Callan and Wilzcek for the global U(1) scalar field model, we study vortex solutions of the Lifshitz-Chern-Simons model formulated on the hyperbolic plane, finding that, as expected, the resulting configurations have finite energy. For completeness, we also explore Lifshitz-Chern-Simons vortex solutions on the sphere.