Multi-spin string solutions in AdS\(_5\times S^5\). (English) Zbl 1031.81051
Summary: 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. A similar solution exists for a string rotating in \(S^5\): it is parametrized by the angular momentum \(J\) of the center of mass and two equal SO(6) angular momenta \(J_2=J_3=J^\prime\) in the two rotation planes. The remarkably simple case is of \(J=0\) where the energy depends on \(J^\prime\) as \(E=\sqrt{(2J')^2+\lambda}\) (\(\lambda\) is the string tension or ’t Hooft coupling). We discuss interpolation of the \(E(J')\) formula to weak coupling by identifying the gauge 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 small fluctuations and stability of these classical solutions and comment on several generalizations.
MSC:
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
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