We compute the meson spectrum of an N = 2 super Yang-Mills theory with fundamental matter from its dual string theory on AdS 5 × S 5 with a D7-brane probe [1]. For scalar and vector mesons with arbitrary R-charge the spectrum is computed in closed form by solving the equations for D7-brane fluctuations; for matter with non-zero mass m q it is discrete, exhibits a mass gap of order m q / √ g s N and furnishes representations of SO(5) even though the manifest global symmetry of the theory is only SO(4). The spectrum of mesons with large spin J is obtained from semiclassical, rotating open strings attached to the D7-brane. It displays Regge-like behaviour for J ≪ √ g s N , whereas for J ≫ √ g s N it corresponds to that of two non-relativistic quarks bound by a Coulomb potential. Meson interactions, baryons and 'giant gauge bosons' are briefly discussed.

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Recently, an impressive agreement was found between anomalous dimensions of certain operators in N = 4 SYM and rotating strings with two angular momenta in the bulk of AdS 5 × S 5 . A one-loop field theory computation, which involves solving a Heisenberg chain by means of the Bethe ansatz agrees with the large angular momentum limit of a rotating string. We point out that the Heisenberg chain can be equally well solved by using a sigma model approach. Moreover we also show that a certain limit, akin to the BMN limit, leads exactly to the same sigma model for a string rotating with large angular momentum. The agreement is then at the level of the action. As an upshot we propose that the rotating string should be identified with a coherent, semi-classical state built out of the eigenstates of the spin chain. The agreement is then complete. For example we show that the mean value of the spin S gives, precisely, the position of the string in the bulk. This suggests a more precise formulation of the AdS/CFT correspondence in the large-N limit and also indicates a way to obtain string theory duals of other gauge theories.

By considering AdS 5 × S 5 string states with large angular momenta in S 5 one is able to provide non-trivial quantitative checks of the AdS/CFT duality. A string rotating in S 5 with two angular momenta J 1 ,J 2 is dual to an operator in N = 4 SYM theory whose conformal dimension can be computed by diagonalizing a (generalization of) spin 1/2 Heisenberg chain Hamiltonian. It was recently argued and verified to lowest order in a large J = J 1 + J 2 expansion, that the Heisenberg chain can be described using a non-relativistic low energy effective 2-d action for a unit vector field n i which exactly matches the corresponding large J limit of the classical AdS 5 × S 5 string action. In this paper we show that this agreement extends to the next order and develop a systematic procedure to compute higher orders in such large angular momentum expansion. This involves several non-trivial steps. On the string side, we need to choose a special gauge with a non-diagonal world-sheet metric which insures that the angular momentum is uniformly distributed along the string, as indeed is the case on the spin chain side. We need also to implement an order by order redefinition of the field n i to get an action linear in the time derivative. On the spin chain side, it turns out to be crucial to include the effects of integrating out short wave-length modes. In this way we gain a better understanding of how (a subsector of) the string sigma model emerges from the dual gauge theory, allowing us to demonstrate the duality beyond comparing particular examples of states with Understanding AdS/CFT duality beyond the BPS or near BPS [1] limit remains an important challenge. It was suggested in [2] that concentrating on string states with large quantum numbers, like angular momentum in AdS 5 , one finds a qualitative (modulo interpolating function of 't Hooft coupling λ) agreement between the AdS 5 string energies and anomalous dimensions of the corresponding gauge theory operators (see also [3,4,5]). About a year ago, it was observed [6] that semiclassical string states with several non-zero angular momenta (with large total S 5 momentum J) have a remarkable property that their energy admits an analytic expansion inλ ≡ λ J 2 at large J. * It was proposed, therefore, that the coefficients of such an expansion can be matched precisely with the perturbative anomalous dimensions of the corresponding scalar SYM operators computed in the same J → ∞,λ < 1 limit [6]. That would provide the first quantitative check of AdS/CFT duality far from the BPS limit. The reason for this expectation was that for such special solutions all string α ′ ∼ 1 √ λ corrections might be suppressed in the large J limit (as was explicitly checked for a particular case in [9]; see also [10] for a review). Then, the classical string energy would represent an exact string theory prediction in this limit. This proposal received a spectacular confirmation in [11,12] where the one-loop anomalous dimensions of the relevant scalar SYM operators were computed utilizing a rema...

Recently, the anomalous dimension of twist two operators in N = 4 SYM theory was computed by Gubser, Klebanov and Polyakov in the limit of large 't Hooft coupling using semi-classical rotating strings in AdS 5 . Here we reproduce their results for large angular momentum by using the cusp anomaly of Wilson loops in Minkowski signature also computed within the AdS/CFT correspondence. In our case the anomalous dimension is related to an Euclidean world-sheet whose properties are completely determined by the symmetries of the problem. This gives support to the proposed identification of rotating strings and twist two operators. 1 See [4] for a review and a complete set of references. 2 See also the recent works [7, 8].