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 × 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 2 Y M 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.

We compute the two-body one-loop effective action for the matrix theory in the pp-wave background, and compare it to the effective action on the supergravity side in the same background. Agreement is found for the effective actions on both sides. This points to the existence of a supersymmetric nonrenormalization theorem in the pp-wave background.

We investigate the gauge/gravity duality in the interaction between two spherical membranes in the 11-dimensional pp-wave background. On the supergravity side, we find the solution to the field equations at locations close to a spherical source membrane, and use it to obtain the light cone Lagrangian of a spherical probe membrane very close to the source, i.e., with their separation much smaller than their radii. On the gauge theory side, using the BMN matrix model, we compute the one-loop effective potential between two membrane fuzzy spheres. Perfect agreement is found between the two sides. Moreover, the one-loop effective potential we obtain on the gauge theory side is valid beyond the small-separation approximation, giving the full interpolation between interactions of membranelike objects and that of graviton-like objects.