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

TL;DR

This paper computes curvature corrections to the spectrum of string theory in AdS_5 x S^5, providing a detailed test of the AdS/CFT correspondence by matching results with N=4 super Yang-Mills theory.

Contribution

It calculates the first curvature corrections to the string spectrum beyond the plane-wave limit, confirming the holographic duality at finite coupling to second order in lambda.

Findings

Spectrum matches gauge theory results to second order in lambda.

Demonstrates a practical method for quantizing superstrings in Ramond-Ramond backgrounds.

Provides detailed spectrum dependence on the coupling constant lambda.

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.