Hidden Virasoro Symmetry of (Soliton Solutions of) the Sine Gordon Theory

TL;DR

This paper constructs a dynamical Virasoro symmetry specific to sine-Gordon soliton solutions, providing explicit transformations and exploring initial steps towards quantization, distinct from space-time conformal symmetry.

Contribution

It introduces a novel dynamical Virasoro symmetry for sine-Gordon solitons and provides explicit local transformation formulas for N-soliton solutions.

Findings

Explicit infinitesimal transformations for N-soliton solutions

Demonstration of locality of the transformations

Initial discussion on quantization of the classical symmetry

Abstract

We present a construction of a Virasoro symmetry of the sine-Gordon (SG) theory. It is a dynamical one and has nothing to do with the space-time Virasoro symmetry of 2D CFT. Although it is clear how it can be realized dyrectly in the SG field theory, we are rather concerned here with the corresponding N-soliton solutions. We present explicit expressions for their infinithesimal transformations and show that they are local in this case. Some preliminary stages about the quantization of the classical results presented in this paper are also given.