Reflection Amplitudes in Non-Simply Laced Toda Theories and Thermodynamic Bethe Ansatz

TL;DR

This paper investigates the ultraviolet behavior of non-simply laced affine Toda theories by calculating reflection amplitudes, deriving quantization conditions, and confirming results with Thermodynamic Bethe Ansatz, revealing insights into their conformal and quantum properties.

Contribution

It provides the first detailed calculation of reflection amplitudes in non-simply laced Toda theories and connects these to TBA results for UV asymptotics.

Findings

Reflection amplitudes computed for non-affine Toda theories.

Quantization conditions derived for vacuum wave functions.

UV asymptotics match TBA predictions.

Abstract

We study the ultraviolet asymptotics in non-simply laced affine Toda theories considering them as perturbed non-affine Toda theories, which possess the extended conformal symmetry. We calculate the reflection amplitudes, in non-affine Toda theories and use them to derive the quantization condition for the vacuum wave function, describing zero-mode dynamics. The solution of this quantization conditions for the ground state energy determines the UV asymptotics of the effective central charge. These asymptotics are in a good agreement with Thermodynamic Bethe Ansatz(TBA) results. To make the comparison with TBA possible, we give the exact relations between parameters of the action and masses of particles as well as the bulk free energies for non-simply laced affine Toda theories.