Multi-spin string solutions in AdS_5 x S^5

TL;DR

This paper constructs and analyzes new multi-spin classical string solutions in AdS_5 x S^5, exploring their energy relations, stability, and potential dual operators in N=4 SYM to extend AdS/CFT correspondence to non-BPS states.

Contribution

It introduces novel multi-spin string solutions with equal spins in AdS_5 and S^5, and discusses their energy spectra, stability, and dual gauge theory operators, expanding the understanding of non-BPS sectors in AdS/CFT.

Findings

New multi-spin string solutions with equal spins in AdS_5 and S^5.

Explicit energy relations for these solutions, including the J=0 case.

Potential dual operators in N=4 SYM and their anomalous dimensions.

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 + {\l}]^{1/2} with {\l}being 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.