Non-planar spin bits beyond two loops

Abstract

We study higher-loop orders of spin bit models underlying the non-planar dynamics of N=4 SYM gauge theory. In particular, we derive a ''tower'' of non-planar identities involving products of site permutation operators. Such identities are then applied in the formulation of planarly consistent, testable conjectures for the full non-planar, higher-loop Hamiltonian of the su(2) spin-chain.

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