We study spin models underlying the non-planar dynamics of 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 gYM2N
but exact in N1.
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 N=4 SYM. Intriguingly, we
identify a sequence of SYM operators for which corrections to the one-loop
anomalous dimensions stop at the first N1 non-planar order.Comment: 22 pages, 2 figures, some typos corrected in eqs. (2.6), (2.8),
(2.11), (2.14