Quantizing three-spin string solution in AdSsi × S 5

Abstract

As was recently found in [3], there exists a simple classical solution describing a closed string rotating in S5 and located at the center of AdS5. 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 ≥ J′, or [J′-J, 0, J′+J] if J′ ≥ J. This solution is stable if J′ ≤ 3/2 J and for large J+2J′ its classical energy admits an expansion in positive powers of λ/(J+2J′)2 (√λ is proportional to string tension): E = J + 2J′ +λ/(J+2J′)2J′ + ⋯. This suggests a possibility of a direct comparison with perturbative SYM results for the corresponding anomalous dimensions in the sector with λ/(J+2J′) 2 ≪ 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 λ. 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. © SISSA/ISAS 2003.