Multi-instanton calculus and the AdS CFT correspondence in N=4 superconformal field theory

We present a self-contained study of ADHM multi-instantons in SU(N) gauge theory, especially the novel interplay with supersymmetry and the large-N limit. We give both field- and string-theoretic derivations of the N = 4 supersymmetric multi-instanton action and collective coordinate integration measure. As a central application, we focus on certain n-point functions G(n), n = 16, 8 or 4, in N = 4 SU(N) gauge theory at the conformal point (as well as on related higher-partial-wave correlators); these are correlators in which the 16 exact supersymmetric and superconformal fermion zero-modes are saturated. In the large-hr limit, for the first time in any four-dimensional theory, we are able to evaluate 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 a single copy of AdS(5) x S-5, (2) The integration measure on this space includes the partition function of ten-dimensional N = 1 SU(k) gauge theory dimensionally reduced to zero dimensions, matching the description of D-instantons in Type IIB string theory. (3) In exact agreement with Spe IIB string calculations, at the k-instanton level, G(n) = root N g(8) k(n-7/2) e(2 pi ik tau) Sigma(d/k) d(-2) . F-n(x(1)...,x(n)), where F-n is identical to a convolution of n bulk-to-boundary supergravity propagators. (C) 1999 Published by Elsevier Science B.V. All rights reserved.