Reflection Amplitudes of ADE Toda Theories and Thermodynamic Bethe Ansatz

TL;DR

This paper investigates the ultraviolet behavior of affine Toda theories by calculating reflection amplitudes, deriving quantization conditions, and confirming results with thermodynamic Bethe ansatz, advancing understanding of these integrable models.

Contribution

It introduces a method to compute reflection amplitudes in affine Toda theories and links them to UV asymptotics and TBA results, providing new insights into their quantum structure.

Findings

Reflection amplitudes relate exponential fields with identical quantum numbers.

Derived quantization conditions for the vacuum wave function.

UV asymptotics agree with thermodynamic Bethe ansatz calculations.

Abstract

We study the ultraviolet asymptotics in affine Toda theories. These models are considered as perturbed non-affine Toda theories. We calculate the reflection amplitudes, which relate different exponential fields with the same quantum numbers. Using these amplitudes we derive the quantization condition for the vacuum wave function, describing zero-mode dynamics, and calculate the UV asymptotics of the effective central charge. These asymptotics are in a good agreement with thermodynamic Bethe ansatz results.