Vortex operator and BKT transition in Abelian duality

• We give a new simple derivation for the sine-Gordon description of Berezinskii-Kosterlitz-Thouless (BKT) phase transition.
• We further develop the Abelian duality of two dimensional continuous field theory in path integral.
• We find that the vortex configurations are naturally mapped to exponential operators (vortex operators) in dual description.
• Our method may be useful for investigating the BKT physics of superconductors.

We give a new simple derivation for the sine-Gordon description of Berezinskii–Kosterlitz–Thouless (BKT) phase transition. 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 relies 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. Since 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.