Abstract
The complete one-loop planar dilatation operator of 
= 4 supersymmetric Yang-Mills is isomorphic to the hamiltonian
of an integrable PSU(2,2|4) quantum spin chain. We construct
the non-linear sigma models describing the continuum limit of the
SU(1|3) and SU(2|3) sectors of the complete = 4 chain. We explicitely identify the spin chain sigma model
with the one for a superstring moving in AdS5 × S5 with
large angular momentum along the five-sphere.
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