Spin chain sigma models with fermions

TL;DR

This paper develops non-linear sigma models for certain sectors of the N=4 supersymmetric Yang-Mills spin chain, linking them to superstring dynamics in AdS_5xS^5 with large angular momentum.

Contribution

It constructs continuum limit sigma models for SU(1|3) and SU(2|3) sectors, connecting spin chain descriptions to superstring theory in AdS_5xS^5.

Findings

Identified the sigma models with superstring motion in AdS_5xS^5

Explicitly constructed the continuum limit of specific sectors

Linked integrable spin chains to string theory dynamics

Abstract

The complete one-loop planar dilatation operator of N=4 supersymmetric Yang-Mills is isomorphic to the hamiltonian of an integrable PSU(2,2|4) quantum spin chain. We construct the non-linear sigma models describing the continuum limit of the SU(1|3) and SU(2|3) sectors of the complete N=4 chain. We explicitely identify the spin chain sigma model with the one for a superstring moving in AdS_5xS^5 with large angular momentum along the five-sphere.