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

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 AdS₅×S⁵ 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 AdS₅×S⁵ about the plane-wave limit. The resulting spectrum has the complete dependence on λ=g_YM²N_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.