# Integrable $\mathfrak{gl}(n|n)$ Toda field theory and its sigma-model dual

## TL;DR

This paper explores the duality between sigma-models and Toda quantum field theories, focusing on the $rak{gl}(n|n)$ affine Toda model's behavior in the strong coupling limit as an $rak{ ilde{CP}}(n-1)$ sigma-model plus a free field.

## Contribution

It demonstrates that the $rak{gl}(n|n)$ affine Toda field theory exhibits a duality with a deformed sigma-model in the strong coupling regime, revealing new insights into their relationship.

## Key findings

- $rak{gl}(n|n)$ Toda theory behaves as a deformed sigma-model at strong coupling
- The duality links Toda QFTs with sigma-models in a novel way
- The model simplifies to a free field plus a sigma-model in the strong coupling limit

## Abstract

In these notes we study the duality between sigma-models and Toda QFT's. We claim that $\mathfrak{gl}(n|n)$ affine Toda field theory behaves in the strong coupling limit as $\eta-$deformed $\mathbb{CP}(n-1)$ sigma-model plus a free field.