Precision spectroscopy of AdS / CFT

We extend recent remarkable progress in the comparison of the dynamical energy spectrum of rotating closed strings in AdS5 ×S 5 and the scaling weights of the corresponding non-near-BPS operators in planar N = 4 supersymmetric gauge theory. On the string side the computations are feasible, using semiclassical methods, if angular momentum quantum numbers are large. This results in a prediction of gauge theory anomalous dimensions to all orders in the ‘t Hooft coupling λ. On the gauge side the direct computation of these dimensions is feasible, using a recently discovered relation to integrable (super) spin chains, provided one considers the lowest order in λ. This oneloop computation then predicts the small-tension limit of the string spectrum for all (i.e. small or large) quantum numbers. In the overlapping window of large quantum numbers and small effective string tension, the string theory and gauge theory results are found to match in a mathematically highly nontrivial fashion. In particular, we compare energies of states with (i) two large angular momenta in S 5 , and (ii) one large angular momentum in AdS5 and S 5 each, and show that the solutions are related by an analytic continuation. Finally, numerical evidence is presented on the gauge side that the agreement persists also at higher (two) loop order.