Multi - instantons and Maldacena's conjecture

Abstract

We examine certain n-point functions Gn in N = 4 supersymmetric SU(N) gauge theory at the conformal point. In the large-N limit, we are able to sum all leading-order multiinstanton contributions exactly. We find compelling evidence for Maldacena’s conjecture: (1) The large-N k-instanton collective coordinate space has the geometry of AdS5 × S5 . (2) In exact agreement with type IIB superstring calculations, at the k-instanton level, Gn = √N g8 kn−7/2e−8n2k/g2Ed|k d−2 · Fn(x1, . . . , xn), where Fn is identical to a convolution of n bulk-to-boundary SUGRA propagators.