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

TL;DR

This paper computes first-order quantum corrections to the classical reflection factor in the sinh-Gordon model with boundary conditions, verifying a conjectured formula and enhancing understanding of boundary effects in integrable quantum field theories.

Contribution

It provides a perturbative calculation of the reflection factor at one loop order, confirming Ghoshal's formula and the dependence on boundary parameters and bulk coupling.

Findings

Quantum corrections align with Ghoshal's formula

Verification of boundary parameter dependence

Consistency with conjectured reflection factor behavior

Abstract

The sinh-Gordon model is restricted to a half-line by boundary conditions maintaining integrability. A perturbative calculation of the reflection factor is given to one loop order in the bulk coupling and to first order in the difference of the two parameters introduced at the boundary, providing a further verification of Ghoshal's formula. The calculation is consistent with a conjecture for the general dependence of the reflection factor on the boundary parameters and the bulk coupling.