Affine Lie Algebra Symmetry of Sine-Gordon Theory at Reflectionless Points

TL;DR

This paper investigates the quantum affine symmetry of the sine-Gordon theory at reflectionless points, demonstrating the local nature of conserved currents and their algebraic structure as affine sl(2).

Contribution

It explicitly constructs conserved currents at reflectionless points and shows they form an affine sl(2) algebra, revealing the underlying symmetry.

Findings

Conserved currents are local at reflectionless points.

Currents satisfy affine sl(2) algebra.

Explicit examples of currents are provided.

Abstract

The quantum affine symmetry of the sine-Gordon theory at q^2 = 1, which occurs at the reflectionless points, is studied. Conserved currents that correspond to the closure of simple root generators are considered, and shown to be local. We argue that they satisfy the affine sl(2) algebra. Examples of these currents are explicitly constructed.