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Spin bit models from non-planar N=4 SYM

S. Bellucci·P. -Y. Casteill·J. F. Morales·C. Sochichiu
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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.

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S. Bellucci, P. -Y. Casteill, J. F. Morales, C. Sochichiu. 2004-07-13. Spin bit models from non-planar N=4 SYM. https://doi.org/10.1016/j.nuclphysb.2004.07.025

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