# Classical and quantum integrable sigma models. Ricci flow, "nice duality" and perturbed rational conformal field theories

## TL;DR

This paper explores classical and quantum integrable sigma models, demonstrating a 'nice' duality property where the dual theory exhibits a weak coupling region, using methods like perturbed CFT, S-matrix, and Bethe Ansatz.

## Contribution

It introduces a duality property for integrable sigma models and formulates the dual theory for deformed CP(n-1), applying various analytical techniques to establish the duality.

## Key findings

- The deformed CP(n-1) sigma model exhibits the 'nice' duality property.
- The dual integrable field theory is explicitly formulated and analyzed.
- Perturbed conformal field theory and Bethe Ansatz confirm the duality.

## Abstract

We consider classical and quantum integrable sigma models and their relations with the solutions of renormalization group equations. We say that an integrable sigma model possesses the "nice" duality property if the dual quantum field theory has the weak coupling region. As an example, we consider the deformed $CP(n-1)$ sigma model with additional quantum degrees of freedom. We formulate the dual integrable field theory and use perturbed conformal field theory, perturbation theory, $S$-matrix, Bethe Ansatz and renormalization group methods to show that this field theory has the "nice" duality property. We consider also an alternative approach to the analysis of sigma models on the deformed symmetric spaces, based on the perturbed rational conformal field theories.