Quantizing String Theory in AdS_5 X S^5: Beyond the pp-Wave

TL;DR

The authors quantify curvature corrections to the plane-wave limit of the type IIB superstring in AdS_5 × S^5 and verify the AdS/CFT correspondence beyond the pp-wave approximation. By explicitly quantizing the Green–Schwarz string in a Ramond–Ramond background and performing first-order degenerate perturbation theory on two-impurity states, they demonstrate exact agreement with the one-loop anomalous dimensions of BMN-type operators in N=4 SYM and reveal the correct N=4 supermultiplet structure. They derive an all-orders-in-$\lambda'$ energy expression for the corrected spectrum and show cancellations that remove normal-ordering ambiguities due to supersymmetry. The results provide strong evidence for the validity of the supercoset-based Green–Schwarz action and pave the way for analyses of higher-impurity sectors and higher-order curvature corrections in the AdS/CFT framework.

Abstract

In a certain kinematic limit, where the effects of spacetime curvature (and other background fields) greatly simplify, the light-cone gauge world-sheet action for a type IIB superstring on AdS_5 x S^5 reduces to that of a free field theory. It has been conjectured by Berenstein, Maldacena, and Nastase that the energy spectrum of this string theory matches the dimensions of operators in the appropriately defined large R-charge large-N_c sector of N=4 supersymmetric Yang--Mills theory in four dimensions. This holographic equivalence is thought to be exact, independent of any simplifying kinematic limits. As a step toward verifying this larger conjecture, we have computed the complete set of first curvature corrections to the spectrum of light-cone gauge string theory that arises in the expansion of AdS_5 x S^5 about the plane-wave limit. The resulting spectrum has the complete dependence on lambda = g_YM^2 N_c; corresponding results in the gauge theory are known only to second order in lambda. We find precise agreement to this order, including the N=4 extended supermultiplet structure. In the process, we demonstrate that the complicated schemes put forward in recent years for defining the Green--Schwarz superstring action in background Ramond-Ramond fields can be reduced to a practical (and correct) method for quantizing the string.