Integrable Spin Chains with U(1)^3 symmetry and generalized Lunin-Maldacena backgrounds

TL;DR

This paper develops a comprehensive framework for three-state spin chains with U(1)^3 symmetry, identifying new integrable models and connecting them to deformations of N=4 SYM and string theory backgrounds.

Contribution

It formulates the coordinate Bethe ansatz, computes the S-matrix, and classifies four classes of integrable models within the most general three-state U(1)^3 symmetric spin chain.

Findings

Identified four classes of integrable models.

Connected known models to a broader family of solutions.

Derived the R-matrix for integrable cases.

Abstract

We consider the most general three-state spin chain with U(1)^3 symmetry and nearest neighbour interaction. Our model contains as a special case the spin chain describing the holomorphic three scalar sector of the three parameter complex deformation of N=4 SYM, dual to type IIB string theory in the generalized Lunin-Maldacena backgrounds discovered by Frolov. We formulate the coordinate space Bethe ansatz, calculate the S-matrix and determine for which choices of parameters the S-matrix fulfills the Yang-Baxter equations. For these choices of parameters we furthermore write down the R-matrix. We find in total four classes of integrable models. In particular, each already known model of the above type is nothing but one in a family of such models.