ar X iv : h ep - t h / 06 04 17 4 v 2 4 M ay 2 00 6 hep - th / Spin - Bits and N = 4 SYM

We briefly review the spin-bit formalism, describing the non-planar dynamics of the N = 4, d = 4 Super Yang-Mills SU(N) gauge theory. After considering its foundations, we apply such a formalism to the su(2) sector of purely scalar operators. In particular, we report an algorithmic formulation of a deplanarizing procedure for local operators in the planar gauge theory, used to obtain planarlyconsistent, testable conjectures for the higher-loop su(2) spin-bit Hamiltonians. Finally, we outlook some possible developments and applications. Contribution to the Proceedings of the 43rd Erice International School of Subnuclear Physics “Towards New Milestones in our Quest to go Beyond the Standard Model” “Ettore Majorana” Foundation and Centre for Scientific Culture, Erice, Italy (29 August–7 September 2005)