Spin bit models from non-planar N=4 SYM

Details Spin bit models from non-planar N=4 SYM Spin bit models from non-planar N=4 SYM

2004-04-08

arxiv.org/abs/hep-th/0404066v2

Nucl.Phys. B699 (2004) 151-173

Physics

High Energy Physics

High Energy Physics - Theory

22 pages, 2 figures, some typos corrected in eqs. (2.6), (2.8), (2.11), (2.14)

Scientific paper

10.1016/j.nuclphysb.2004.07.025

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.

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