Spin bit models from non-planar N=4 SYM

TL;DR

This paper develops a non-local spin chain model to analyze non-planar dynamics and operator mixing in ${ m N}=4$ SYM, revealing operators with anomalous dimensions unaffected beyond first non-planar correction.

Contribution

It introduces a novel non-local spin chain Hamiltonian that captures non-planar effects exactly in ${1/N}$ and applies it to study anomalous dimensions and operator mixing.

Findings

Derived a non-local spin chain Hamiltonian for non-planar ${ m N}=4$ SYM.

Identified operators with anomalous dimensions stopping at first ${1/N}$ correction.

Provided a systematic framework for non-planar operator analysis.

Abstract

We study spin models underlying the non-planar dynamics of ${\cal N}=4$ SYM gauge theory. In particular, we derive the non-local spin chain Hamiltonian generating dilatations in the gauge theory at leading order in $g_{\rm YM}^2 N$ but exact in ${1\over N}$. States in the spin chain are characterized by a spin-configuration and a linking variable describing how sites in the chain are connected. Joining and splitting of string/traces are mimicked by a twist operator acting on the linking variable. The results are applied to a systematic study of non-planar anomalous dimensions and operator mixing in ${\cal N}=4$ SYM. Intriguingly, we identify a sequence of SYM operators for which corrections to the one-loop anomalous dimensions stop at the first ${1\over N}$ non-planar order.