# Quantum Inverse Scattering and the Lambda Deformed Principal Chiral Model

## TL;DR

This paper develops a method to quantize the lambda model, a deformed integrable field theory, by deforming its symplectic structure to achieve ultra-locality, enabling lattice quantization and application of the quantum inverse scattering method.

## Contribution

It introduces a symplectic deformation approach that transforms the lambda model into an ultra-local lattice spin chain, facilitating its quantization and analysis.

## Key findings

- The deformed lattice theory is a generalized spin chain solvable by algebraic Bethe Ansatz.
- The IR limit of the lattice model belongs to the same universality class as the lambda model.
- The approach potentially extends to other lambda models and string world-sheet theories.

## Abstract

The lambda model is a one parameter deformation of the principal chiral model that arises when regularizing the non-compactness of a non-abelian T dual in string theory. It is a current-current deformation of a WZW model that is known to be integrable at the classical and quantum level. The standard techniques of the quantum inverse scattering method cannot be applied because the Poisson bracket is non ultra-local. Inspired by an approach of Faddeev and Reshetikhin, we show that in this class of models, there is a way to deform the symplectic structure of the theory leading to a much simpler theory that is ultra-local and can be quantized on the lattice whilst preserving integrability. This lattice theory takes the form of a generalized spin chain that can be solved by standard algebraic Bethe Ansatz techniques. We then argue that the IR limit of the lattice theory lies in the universality class of the lambda model implying that the spin chain provides a way to apply the quantum inverse scattering method to this non ultra-local theory. This points to a way of applying the same ideas to other lambda models and potentially the string world-sheet theory in the gauge-gravity correspondence.