Second order quantum corrections to the classical reflection factor of the sinh-Gordon model

TL;DR

This paper calculates second order quantum corrections to the classical reflection factor in the sinh-Gordon model with boundary conditions, confirming consistency with Ghoshal's formula through perturbation theory.

Contribution

It provides the first detailed second order quantum correction analysis of the reflection factor in the sinh-Gordon model with boundary conditions.

Findings

Second order quantum corrections are consistent with Ghoshal's formula.

Quantum corrections are computed up to one loop order in the bulk coupling.

Results enhance understanding of boundary effects in integrable quantum field theories.

Abstract

The sinh-Gordon model on a half-line with integrable boundary conditions is considered in low order perturbation theory developed in affine Toda field theory. The quantum corrections to the classical reflection factor of the model are studied up to the second order in the difference of the two boundary parameters and to one loop order in the bulk coupling. It is noticed that the general form of the second order quantum corrections are consistent with Ghoshal's formula.