Integrable Inhomogeneous Spin Chains in Generalized Lunin-Maldacena Backgrounds

TL;DR

This paper provides an exact solution for the most general inhomogeneous spin chain with specific symmetries, related to deformed N=4 SYM theory and string theory backgrounds, extending previous homogeneous models.

Contribution

It introduces a Matrix Product Ansatz solution for inhomogeneous spin chains with $U(1)^2$ and $U(1)^3$ symmetries, generalizing earlier homogeneous models.

Findings

Exact solutions for inhomogeneous spin chains with $U(1)^2$ and $U(1)^3$ symmetries.

Connections to one-loop mixing matrices in Leigh-Strassler deformed N=4 SYM.

Extension of previous homogeneous spin chain results.

Abstract

We obtain through a Matrix Product Ansatz the exact solution of the most general inhomogeneous spin chain with nearest neighbor interaction and with $U(1)^2$ and $U(1)^3$ symmetries. These models are related to the one loop mixing matrix of the Leigh-Strassler deformed N=4 SYM theory, dual to type IIB string theory in the generalized Lunin-Maldacena backgrounds, in the sectors of two and three kinds of fields, respectively. The solutions presented here generalizes the results obtained by the author in a previous work for homogeneous spins chains with $U(1)^N$ symmetries in the sectors of N=2 and N=3.