A note on spin chain/string duality

TL;DR

This paper explores the connection between spin chain models and string theory in the context of N=4 SYM, generalizing previous solutions and relating them to integrable systems, thereby advancing the understanding of the gauge/string duality.

Contribution

It generalizes Kruczenski's sigma model approach to solving the Heisenberg spin chain and links the solutions to the Neumann-Rosochatius integrable system, enhancing the spin chain/string duality understanding.

Findings

Solutions related to the Neumann-Rosochatius system were obtained.

The work comments on the dual string theory interpretation.

It extends the sigma model approach to more general spin chain solutions.

Abstract

Recently a significant progress in matching the anomalous dimensions of certain class of operators in N=4 SYM theory and rotating strings was made. The correspondence was established mainly using Bethe ansatz technique applied to the spin s Heisenberg model. In a recent paper Kruczenski (hep-th/0311203) suggested to solve the Heisenberg model by using of sigme model approach. In this paper we generalize the solutions obtained by Kruczenski and comment on the dual string theory. It turns out that our solutions are related to the so called Neumann-Rosochatius integrable system. We comment on the spin chain solutions and on the string/gauge theory correspondence.