Multi-Instanton Calculus and the AdS/CFT Correspondence in N=4 Superconformal Field Theory

TL;DR

The paper provides a comprehensive, self-contained analysis of ADHM multi-instantons in ${\cal N}=4$ SU(N) gauge theory, combining field-theoretic and D-brane perspectives and placing them in the large-$N$ context to test Maldacena’s AdS/CFT conjecture. A central result is that, at large $N$, the leading multi-instanton contributions organize around a single $AdS_5\times S^5$ moduli space, with the integration measure factoring into the $AdS_5\times S^5$ volume and the partition function of a ten-dimensional ${\cal N}=1$ $SU(k)$ matrix model, precisely matching D-instanton physics on the IIB side. The authors compute exact leading semiclassical contributions to the sixteen-, eight-, and four-fermion correlators $G_n$ and show exact agreement with the corresponding IIB predictions, including KK-mode extensions on $S^5$. These results constitute compelling circumstantial evidence for the AdS/CFT correspondence in a nontrivial, nonperturbative sector and reveal deep connections between large-$N$ gauge theory, ADHM instanton calculus, and string-theoretic D-instantons. The work also highlights the emergence of ten-dimensional geometry and matrix-model structure from purely four-dimensional gauge dynamics in the large-$N$ limit.

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 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-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 AdS_5 x S^5. (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, G_n = \sqrt{N} g^8 k^{n-7/2} e^{2πikτ} \sum_{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.