Precision Spectroscopy of AdS/CFT

TL;DR

This paper compares the energy spectrum of rotating strings in AdS_5xS^5 with the scaling dimensions of operators in N=4 supersymmetric gauge theory, showing remarkable agreement in certain regimes and extending the understanding of AdS/CFT correspondence.

Contribution

It extends the comparison of string spectra and gauge theory dimensions to all orders in coupling, using semiclassical and integrability methods, and provides evidence for agreement beyond one-loop.

Findings

Matching of string and gauge theory spectra in large quantum number regime

Analytic continuation relates different state configurations

Numerical evidence supports higher-loop agreement

Abstract

We extend recent remarkable progress in the comparison of the dynamical energy spectrum of rotating closed strings in AdS_5xS^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 lambda. 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 lambda. This one-loop 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 non-trivial fashion. In particular, we compare energies of states with (i) two large angular momenta in S^5, and (ii) one large angular momentum in AdS_5 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.