Large spin limits of AdS/CFT and generalized Landau-Lifshitz equations

We consider AdS(5) x S-5 string states with several large angular momenta along AdS(5) and S-5 directions which are dual to single-trace Super-Yang-Mills (SYM) operators built out of chiral combinations of scalars and covariant derivatives. In particular, we focus on the SU(3) sector (with three spins in S-5) and the SL(2) sector (with one spin in AdS(5) and one in S-5), generalizing recent work [1] and [2] on the SU(2) sector with two spins in S-5. We show that, in the large spin limit and at leading order in the effective coupling expansion, the string sigma model equations of motion reduce to matrix Landau-Lifshitz equations. We then demonstrate that the coherent-state expectation value of the one-loop SYM dilatation operator restricted to the corresponding sector of single trace operators is also effectively described by the same equations. This implies a universal leading order equivalence between string energies and SYM anomalous dimensions, as well as a matching of integrable structures. We also discuss the more general 5-spin sector and comment on SO(6) states dual to non-chiral scalar operators.