Quantizing three-spin string solution inAdS5×S5

As was recently found in hep-th/0304255, there exists a simplenon-supersymmetric classical solution describing a closed string rotating inS^5 and located at the center of AdS_5. It is parametrized by the angularmomentum J of the center of mass and two equal SO(6) angular momenta J' in thetwo other orthogonal rotation planes. The dual N=4 SYM operators should bescalar operators in SU(4) representations [0,J-J',2J'] or [J'-J,0,J'+J]. Thissolution is stable if J' > 3/2 J and for large J + 2 J' its classical energyadmits an expansion in positive powers of g_eff = \lambda/(J + 2 J')^2: E= J +2 J' + g_eff J' + ... . This suggests a possibility of a direct comparison withperturbative SYM results for the corresponding anomalous dimensions in thesector with g_eff << 1, by analogy with the BMN case. We conjecture that allquantum sigma model string corrections are then subleading at large J', so thatthe classical formula for the energy is effectively exact to all orders in\lambda. It could then be interpolated to weak coupling, representing aprediction for the anomalous dimensions on the SYM side. We test thisconjecture by computing the 1-loop superstring sigma model correction to theclassical energy.Comment: 25 pages, harvmac. v5: minor misprints in eqs (2.6),(2.16),(2.20),(2.21) correcte