Quantizing three-spin string solution in AdS5 x S5 -: art. no. 016

As was recently found in [3], there exists a simple classical solution describing a closed string rotating in S-5 and located at the center of AdS(5). It is parametrized by the angular momentum J of the center of mass and two equal SO(6) angular momenta J' in the two other orthogonal rotation planes. The corresponding dual N = 4 SYM operators should be scalar operators in SU(4) representations [0, J - J', 2J'] if J greater than or equal to J', or [J' - J, 0, J' + J] if J' greater than or equal to J. This solution is stable if J' less than or equal to 3/2J and for large J + 2J' its classical energy admits an expansion in positive powers of lambda/(J+2J')(2) (root(lambda) over bar is proportional to string tension): E = J + 2J'+ lambda (J+2J')(2) J' + .... This suggests a possibility of a direct comparison with perturbative SYM results for the corresponding anomalous dimensions in the sector with lambda (J+2J')(2) much less than 1, by analogy with the BMN case. We conjecture that all quantum sigma model string corrections are then subleading at large J', so that the classical formula for the energy is effectively exact to all orders in lambda. It could then be interpolated to weak coupling, representing a prediction for the anomalous dimensions on the SYM side. We test this conjecture by computing the 1-loop superstring sigma model correction to the classical energy.