We study vortexlike solutions to the Lifshitz-Chern-Simons theory. We find that such solutions exist 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.

• Received 19 June 2012

DOI:https://doi.org/10.1103/PhysRevD.87.025031