Multi-Instantons and Maldacena's Conjecture

Abstract

We examine certain n-point functions G_n in {\cal N}=4 supersymmetric SU(N) gauge theory at the conformal point. In the large-N limit, we are able to sum all leading-order multi-instanton contributions exactly. We find compelling evidence for Maldacena's conjecture: (1) The large-N k-instanton collective coordinate space has the geometry of AdS_5 x S^5. (2) In exact agreement with type IIB superstring calculations, at the k-instanton level, $G_n=\sqrt{N}{g}^8{k}^{n-7/2}{e}^{-8{\pi }^{2}k/g^2}{\sum }_{d|k}{d}^{-2}\times F_n(x_1,...,x_n)$, where F_n is identical to a convolution of n bulk-to-boundary SUGRA propagators.

Comments: 12 pp. In this version we use the recently-calculated normalization for the 10D partition function of N=1 SYM. Consequently, we can now claim perfect agreement between N=4 large-N SQCD, and type IIB SUGRA on AdS_5 x S^5