The SU(3) spin chain sigma model and string theory

TL;DR

This paper constructs a sigma model from the SU(3) spin chain in N=4 SYM and shows its correspondence to string theory in AdS_5xS^5, matching energies and spectra of rotating strings.

Contribution

It develops a continuum sigma model for the SU(3) spin chain and demonstrates its equivalence to string dynamics in the five-sphere, linking gauge theory and string theory.

Findings

Sigma model describes the continuum limit of the SU(3) spin chain.

Spectrum of rotating strings matches the sigma model predictions.

Energy calculations agree with string theory results.

Abstract

The ferromagnetic integrable SU(3) spin chain provides the one loop anomalous dimension of single trace operators involving the three complex scalars of N=4 supersymmetric Yang-Mills. We construct the non-linear sigma model describing the continuum limit of the SU(3) spin chain. We find that this sigma model corresponds to a string moving with large angular momentum in the five-sphere in AdS_5xS^5. The energy and spectrum of fluctuations for rotating circular strings with angular momenta along three orthogonal directions of the five-sphere is reproduced as a particular case from the spin chain sigma model.