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

Abstract

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 Gn, 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-N limit, for the first time in any 4-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 AdS5 × S5 . (2) The integration measure on this space includes the partition function of 10-dimensional N = 1 SU(k) gauge theory dimensionally reduced to 0 dimensions, matching the description of D-instantons in Type IIB string theory. (3) In exact agreement with Type IIB string calculations, at the k-instanton level, Gn = √N g8 kn−7/2e2nikt Ed|k d−2 · Fn(x1, . . . , xn), where Fn is identical to a convolution of n bulk-to-boundary supergravity propagators.