Precision spectroscopy of AdS/CFT

We extend recent remarkable progress in the comparison of the dynamicalenergy spectrum of rotating closed strings in AdS_5xS^5 and the scaling weightsof the corresponding non-near-BPS operators in planar N=4 supersymmetric gaugetheory. On the string side the computations are feasible, using semiclassicalmethods, if angular momentum quantum numbers are large. This results in aprediction of gauge theory anomalous dimensions to all orders in the `t Hooftcoupling lambda. On the gauge side the direct computation of these dimensionsis feasible, using a recently discovered relation to integrable (super) spinchains, provided one considers the lowest order in lambda. This one-loopcomputation then predicts the small-tension limit of the string spectrum forall (i.e. small or large) quantum numbers. In the overlapping window of largequantum numbers and small effective string tension, the string theory and gaugetheory results are found to match in a mathematically highly non-trivialfashion. In particular, we compare energies of states with (i) two largeangular momenta in S^5, and (ii) one large angular momentum in AdS_5 and S^5each, and show that the solutions are related by an analytic continuation.Finally, numerical evidence is presented on the gauge side that the agreementpersists also at higher (two) loop order.Comment: 26 pages, 1 figure, v2: typos correcte