Spin-Bits and N=4 SYM

Abstract

We briefly review the spin-bit formalism, describing the non-planar dynamics of the $\mathcal{N}=4,d=4$ 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 planarly-consistent, testable conjectures for the higher-loop $su(2)$ spin-bit Hamiltonians. Finally, we outlook some possible developments and applications.

29 pages; 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'', Erice, Italy (29 August--7 September 2005); v2: some references added