Quantizing string theory in AdS5× S5: beyond the pp-wave

Abstract

In a certain kinematic limit, where the effects of spacetime curvature (and other background fields) greatly simplify, the light-cone gauge worldsheet action for a type IIB superstring on AdS 5× 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× S 5 about the plane-wave limit. The resulting spectrum has the complete dependence on λ= g YM 2 N c ; corresponding results in the gauge theory are known only to second order in λ. 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.