%0 Journal Article %A Hernández Redondo, Rafael %A López, Esperanza %T Spin chain sigma models with fermions %D 2004 %@ 1126-6708 %U https://hdl.handle.net/20.500.14352/52161 %X The complete one-loop planar dilatation operator of N = 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 N = 4 chain. We explicitely identify the spin chain sigma model with the one for a superstring moving in AdS 5 × S 5 with large angular momentum along the five-sphere. %~