Duality in Complex sine-Gordon Theory

TL;DR

This paper explores new aspects of the complex sine-Gordon theory by reformulating it via gauged Wess-Zumino-Witten action, establishing a duality between different coupling regimes, and deriving exact solutions like solitons and breathers.

Contribution

It introduces a dual transformation in complex sine-Gordon theory, connecting different coupling constants, and provides explicit solutions and insights into soliton charge structures.

Findings

Duality between positive and negative coupling constants.

Explicit Bäcklund transform and superposition rule.

Classification of solitons as topological or non-topological.

Abstract

New aspects of the complex sine-Gordon theory are addressed through the reformulation of the theory in terms of the gauged Wess-Zumino-Witten action. A dual transformation between the theory for the coupling constant $\b > 0$ and the theory for $\b < 0$ is given which agrees with the Krammers-Wannier duality in the context of perturbed conformal field theory. The B\"{a}cklund transform and the nonlinear superposition rule for the complex sine-Gordon theory are presented and from which, exact solutions, solitons and breathers with U(1) charge, are derived. We clarify topological and nontopological nature of neutral and charged solitons respectively, and discuss about the duality between the vector and the axial U(1) charges.