Review of AdS/CFT Integrability, Chapter I.3: Long-range spin chains

TL;DR

This paper reviews recent progress in the theory of long-range integrable spin chains, emphasizing their significance in AdS/CFT correspondence where they model the dilatation operator.

Contribution

It provides a concise overview of the developments in long-range spin chains and their role in understanding integrability in AdS/CFT.

Findings

Long-range spin chains generalize nearest-neighbour models.

They are relevant to the integrability of the AdS/CFT dilatation operator.

Recent theoretical advancements have clarified their structure.

Abstract

In this contribution we briefly review recent developments in the theory of long-range integrable spin chains. These spin chains constitute a natural generalisation of the well-studied integrable nearest-neighbour chains and are of particular relevance to the integrability in the AdS/CFT correspondence since the dilatation operator in the asymptotic region is conjectured to be a Hamiltonian of an integrable long-range psu spin chain.