On the Structure of the Dilatation Operator in N=4 SYM"

A sector of N=4 SYM can be represented by an SU(2) spin chain, whose Hamiltonian H is the dilatation operator of the d=4 theory. This H acts on spins by permuting them, so one can organize H according to the number of spins participating in a given permutation. The simplest permutation involves two spins, and to determine this part of H it is enough to demand a good classical limit and matching with the BMN story. We do not compute a single Feynman diagram; instead, this result is entirely a prediction of AdS/CFT.