Hidden Virasoro Symmetry of the Sine Gordon Theory

TL;DR

This paper constructs a novel non-local Virasoro symmetry within the Sine-Gordon theory that acts locally on soliton variables, revealing new geometric insights and potential quantization pathways.

Contribution

It introduces a new dynamical Virasoro symmetry in Sine-Gordon theory that is distinct from the space-time conformal symmetry, with local action on soliton variables.

Findings

Defines a non-local Virasoro symmetry in SG theory.

Shows the symmetry acts locally on N-soliton variables.

Provides initial insights into quantization of the symmetry.

Abstract

In the framework of the Sine-Gordon (SG) theory we will present the construction of a dynamical Virasoro symmetry which has nothing to do with the space-time Virasoro symmetry of 2D CFT. Although, it is non-local in the SG field theory, nevertheless it gives rise to a local action on specific N-soliton solution variables. These {\it analytic} variables possess a beautiful geometrical meaning and enter the Form Factor expressions. At the end, we will also give some preliminary hints about the quantisation.