Integrability, Duality and Sigma Models

TL;DR

This paper explores conformal field theories with W-algebras that lead to integrable quantum field theories, establishing their duality with deformations of O(N) sigma models through various theoretical approaches.

Contribution

It introduces a class of conformal field theories with W-algebras, constructs their integrable perturbations, and demonstrates their duality with deformed O(N) sigma models.

Findings

QFTs possess local and non-local integrals of motion

The S-matrix matches the O(N) sigma model in strong coupling

Perturbation theory and Bethe ansatz confirm duality

Abstract

We introduce and study conformal field theories specified by $W-$algebras commuting with certain set of screening charges. These CFT's possess perturbations which define integrable QFT's. We establish that these QFT's have local and non-local Integrals of Motion and admit the perturbation theory in the weak coupling region. We construct factorized scattering theory which is consistent with non-local Integrals of Motion and perturbation theory. In the strong coupling limit the $S-$matrix of this QFT tends to the scattering matrix of the $O(N)$ sigma model. The perturbation theory, Bethe anzatz technique, renormalization group approach and methods of conformal field theory are applied to show, that the constructed QFT's are dual to integrable deformation of $O(N)$ sigma-models.