The Vortex Solution in the (2+1)-Dimensional Yang-Mills-Chern-Simons Theory at High Temperature

TL;DR

This paper presents a finite-energy vortex solution in a (2+1)-dimensional SU(2) gauge theory with Chern-Simons term at high temperature, revealing a ground state configuration with quantized flux.

Contribution

It derives a novel vortex solution at high temperature from the effective Lagrangian, incorporating finite temperature corrections, and analyzes its properties and implications.

Findings

Vortex has finite energy and quantized magnetic flux.

Vortex is neutral overall with localized charge at the center.

At high temperature, the vortex corresponds to the ground state.

Abstract

The vortex-like solution to the non-linear field equations in a two-dimensional SU(2) gauge theory with the Chern-Simons mass term is found at high temperature. It is derived from the effective Lagrangian including the leading order finite temperature corrections. The discovered field configuration possesses the finite energy and the quantized magnetic flux. At the centre of the vortex the point charge is located which is surrounded by the distributed charge of the opposite sign and the vortex is neutral as a whole. At high temperature the energy of the vortex is negative and it corresponds to the ground state. The derived solution is considered to be a result of heating the lattice vacuum structure formed at zero temperature.