Vortex Operator and BKT Transition in Abelian Duality

TL;DR

This paper presents a simplified, continuous field theoretic derivation of the BKT transition using Abelian duality, connecting vortex configurations to exponential operators in the sine-Gordon model.

Contribution

It introduces a new, simpler derivation of the BKT transition based on Abelian duality and path integration, differing from traditional lattice or Coulomb gas methods.

Findings

Vortex configurations map to exponential operators in dual theory

Derivation is simpler and continuous compared to traditional methods

Potential applications to superconductors' BKT physics

Abstract

We give a new simple derivation for the sine-Gordon description of Berezinskii-Kosterlitz-Thouless(BKT) phase transition (is driven by vortices). Our derivation is simpler than traditional derivations. Besides, our derivation is a continuous field theoretic derivation by using path integration, different from the traditional derivations which are based on lattice theory or based on Coulomb gas model. Our new derivation rely on Abelian duality of two dimensional quantum field theory. By utilizing this duality in path integration, we find that the vortex configurations are naturally mapped to exponential operators in dual description, these operators are the vortex operators that can create vortices, the sine-Gordon description then naturally follows. Our method may be useful for the investigation to the BKT physics of superconductors.