Quantum corrections to the classical reflection factor in A2(1) Toda Field Theory

TL;DR

This paper calculates the quantum correction to the classical reflection factor in affine Toda field theory and confirms it matches the conjectured exact result, exploring implications for boundary conditions and duality.

Contribution

It provides the first perturbative calculation of quantum corrections to the reflection factor in $a_2^{(1)}$ affine Toda field theory and compares it with the conjectured exact solution.

Findings

Quantum correction agrees with the conjectured exact reflection factor.

Existence of other exact reflection factors consistent with perturbative results.

Exploration of duality transformations relating different boundary conditions.

Abstract

The $O(\beta^2)$ quantum correction to the classical reflection factor is calculated for one of the integrable boundary conditions of $a_2^{(1)}$ affine Toda field theory. This is found to agree with the conjectured exact reflection factor of the quantum theory. We consider the existence of other exact reflection factors consistent with our perturbative answer and examine the question of how duality transformations might relate theories with different boundary conditions.