Multi-spin string solutions in AdS_5 x S^5

Abstract

Motivated by attempts to extend AdS/CFT duality to non-BPS states we consider classical closed string solutions with several angular momenta in different directions of AdS_5 and S^5. We find a novel solution describing a circular closed string located at a fixed value of AdS_5 radius while rotating simultaneously in two planes in AdS_5 with equal spins S. This solution is a direct generalization of a two-spin flat-space solution where the string rotates in two orthogonal planes while always lying on a 3-sphere. Similar solution exists for a string rotating in S^5: it is parametrized by the angular momentum J of the center of mass and the two equal SO(6) angular momenta J_2=J_3=J' in the two rotation planes. The remarkably simple case is of J=0 where the energy depends on J' as E=[(2J')^2 + ł]^{1/2} with łbeing the string tension or `t Hooft coupling. We discuss interpolation of the E(J') relation to weak coupling by identifying the N=4 SYM theory operator that should be dual to the corresponding semiclassical string state and utilizing existing results for its perturbative anomalous dimension. This opens up a possibility of studying AdS/CFT duality in this new non-BPS sector. We also investigate stability of these classical solutions under small perturbations and comment on several generalizations.

39 pages, harvmac; v2: minor corrections and new remarks in sections 4.1 and 5; new appendix D and references added. v3: discussion of stability of solutions corrected (sections 1, 3.2, 4.3 and appendix A)

References in corpus (3)

• The Dilatation Operator of Conformal N=4 Super Yang-Mills Theory
• Gauge/string duality for QCD conformal operators
• Solvable models of strings in homogeneous plane wave backgrounds

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