From Reflection Amplitudes to One-point Functions in Non-simply Laced Affine Toda Theories and Applications to Coupled Minimal Models

TL;DR

This paper computes reflection amplitudes and one-point functions in non-simply laced affine Toda theories, applying these results to analyze correlation functions in coupled minimal models with various central charges.

Contribution

It introduces a method to derive vacuum expectation values in non-simply laced affine Toda theories using reflection relations, extending understanding of their correlation functions.

Findings

Calculated reflection amplitudes for non-affine Toda theories.

Derived vacuum expectation values for dual pairs of affine Toda theories.

Predicted correlation functions in coupled minimal models with different central charges.

Abstract

The reflection amplitudes in non-affine Toda theories which possess extended conformal symmetry are calculated. Considering affine Toda theories as perturbed non-affine Toda theories and using reflection relations which relate different fields with the same conformal dimension, we deduce the vacuum expectation values of local fields for all dual pairs of non-simply laced affine Toda field theories. As an application, we calculate the leading term in the short and long distance predictions of the two-point correlation functions in the massive phase of two coupled minimal models. The central charge of the unperturbed models ranges from $c=1$ to $c=2$, where the perturbed models correspond to two magnetically coupled Ising models and Heisenberg spin ladders, respectively.