# Yang Baxter and Anisotropic Sigma and Lambda Models, Cyclic RG and Exact S-Matrices

## TL;DR

This paper studies integrable deformations of SU(2) sigma and lambda models, revealing cyclic RG behavior and proposing exact S-matrices that describe scattering in these models, with implications for quantum symmetries and dualities.

## Contribution

It introduces exact S-matrices for anisotropic deformations of sigma and lambda models, highlighting cyclic RG flows and complex quantum group symmetries.

## Key findings

- XXZ deformations are UV safe in one regime
- Yang-Baxter deformations exhibit cyclic RG behavior
- Proposed S-matrices are periodic in rapidity and violate parity at large rapidity

## Abstract

Integrable deformation of SU(2) sigma and lambda models are considered at the classical and quantum levels. These are the Yang-Baxter and XXZ-type anisotropic deformations. The XXZ type deformations are UV safe in one regime, while in another regime, like the Yang-Baxter deformations, they exhibit cyclic RG behaviour. The associated affine quantum group symmetry, realized classically at the Poisson bracket level, has q a complex phase in the UV safe regime and q real in the cyclic RG regime, where q is an RG invariant. Based on the symmetries and RG flow we propose exact factorizable S-matrices to describe the scattering of states in the lambda models, from which the sigma models follow by taking a limit and non-abelian T-duality. In the cyclic RG regimes, the S-matrices are periodic functions of rapidity, at large rapidity, and in the Yang-Baxter case violate parity.