(Semi)classical analysis of sine-Gordon theory on a strip

TL;DR

This paper analyzes classical sine-Gordon theory on a strip with integrable boundary conditions, exploring static solutions, their stability, and finite volume effects, connecting classical results with quantum expectations.

Contribution

It derives classical Bethe-Yang quantization conditions and finite volume corrections, bridging classical analysis with quantum integrable field theory insights.

Findings

Derived classical Bethe-Yang quantization conditions.

Analyzed ground state stability and energy dependence on volume.

Established classical limit of Luscher type formulas.

Abstract

Classical sine-Gordon theory on a strip with integrable boundary conditions is considered analyzing the static (ground state) solutions, their existence, energy and stability under small perturbations. The classical analogue of Bethe-Yang quantization conditions for the (linearized) first breather is derived, and the dynamics of the ground states is investigated as a function of the volume. The results are shown to be consistent with the expectations from the quantum theory, as treated in the perturbed conformal field theory framework using the truncated conformal space method and thermodynamic Bethe Ansatz. The asymptotic form of the finite volume corrections to the ground state energies is also derived, which must be regarded as the classical limit of some (as yet unknown) Luscher type formula.