Normalization Factors, Reflection Amplitudes and Integrable Systems

TL;DR

This paper computes normalization factors and reflection amplitudes in conformal and affine Toda field theories, deriving vacuum expectation values and boundary amplitudes, with applications to statistical models and topological field theories.

Contribution

It introduces new calculations of reflection amplitudes and vacuum expectation values in integrable conformal and Toda theories, including boundary effects and duality properties.

Findings

Explicit vacuum expectation values for exponential fields in affine Toda theories

Boundary reflection amplitudes and one-point functions in Toda models

Asymptotic analysis of solutions in topological field theories

Abstract

We calculate normalization factors and reflection amplitudes in the W-invariant conformal quantum field theories. Using these CFT data we derive vacuum expectation values of exponential fields in affine Toda theories and related perturbed conformal field theories. We apply these results to evaluate explicitly the expectation values of order parameters in the field theories associated with statistical systems, like XY, Z_n-Ising and Ashkin-Teller models. The same results are used for the calculation of the asymptotics of cylindrically symmetric solutions of the classical Toda equations which appear in topological field theories. The integrable boundary Toda theories are considered. We derive boundary reflection amplitudes in non-affine case and boundary one point functions in affine Toda theories. The boundary ground state energies are cojectured. In the last section we describe the duality properties and calculate the reflection amplitudes in integrable deformed Toda theories.