Normalization Factors, Reflection Amplitudes and Integrable Systems

Abstract

The integrable systems associated with affine and nonaffine Toda theories are considered. We calculate normalization factors and reflection amplitudes in 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 the XY, Z _n -Ising and Ashkin-Teller models. The same results are used to calculate the asymptotics of cylindrically symmetric solutions of the classical Toda equations which appear in topological field theories. Integrable boundary Toda theories are also considered. We derive boundary reflection amplitudes in the nonaffine case and boundary one-point functions in affine Toda theories. The boundary ground state energies are conjectured. In the last section we describe the duality properties and calculate the reflection amplitudes in integrable deformed Toda theories.