We study the ultraviolet asymptotics in An 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.
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We thank V. Fateev and Al. Zamolodchikov for valuable discussions and Univ. Montpellier II, CNRS, and KIAS for hospitality. The work of C.K. was supported by the BK21 project of the Ministry of Education. This work is supported in part by KOSEF 1999-2-112-001-5 (CA,CR) and MOST-99-N6-01-01-A-5 (CA).