Reflection Amplitudes of Boundary Toda Theories and Thermodynamic Bethe Ansatz

TL;DR

This paper investigates the ultraviolet behavior of boundary affine Toda theories, comparing reflection amplitude methods with thermodynamic Bethe ansatz results to validate boundary scattering amplitudes and vacuum energy conjectures.

Contribution

It provides a non-perturbative validation of boundary scattering amplitudes and vacuum energies in affine Toda theories using two independent approaches.

Findings

Reflection amplitudes match thermodynamic Bethe ansatz results

Boundary vacuum energies are confirmed

Duality between boundary conditions is supported

Abstract

We study the ultraviolet asymptotics in $A_n$ affine Toda theories with integrable boundary actions. The reflection amplitudes of non-affine Toda theories in the presence of conformal boundary actions have been obtained from the quantum mechanical reflections of the wave functional in the Weyl chamber and used for the quantization conditions and ground-state energies. We compare these results with the thermodynamic Bethe ansatz derived from both the bulk and (conjectured) boundary scattering amplitudes. The two independent approaches match very well and provide the non-perturbative checks of the boundary scattering amplitudes for Neumann and $(+)$ boundary conditions. Our results also confirm the conjectured boundary vacuum energies and the duality conjecture between the two boundary conditions.