Exact form factors for the scaling Z{N}-Ising and the affine A{N-1}-Toda quantum field theories

TL;DR

This paper extends the calculation of exact form factors to the Z_N-Ising and affine A_{N-1}-Toda quantum field theories, providing explicit formulas for various operators and confirming their quantum equations of motion.

Contribution

It introduces explicit form factors for Z_N-Ising and affine A_{N-1}-Toda models, including order, disorder, para-fermi fields, and exponential Toda fields, with proofs of equations of motion and renormalizations.

Findings

Explicit form factors for Z_N-Ising model operators.

Form factors for exponential Toda fields.

Proof of quantum equations of motion and exact renormalizations.

Abstract

Previous results on form factors for the scaling Ising and the sinh-Gordon models are extended to general $Z_{N}$-Ising and affine $A_{N-1}$-Toda quantum field theories. In particular result for order, disorder parameters and para-fermi fields $\sigma_{Q}(x), \mu_{\tilde{Q}}(x)$ and $\psi_{Q}(x)$ are presented for the $Z_{N}$-model. For the $A_{N-1}$-Toda model all form factors for exponentials of the Toda fields are proposed. The quantum field equation of motion is proved and the mass and wave function renormalization are calculated exactly.