Multi-Instantons and Maldacena's Conjecture

TL;DR

This paper provides exact calculations of multi-instanton contributions in N=4 supersymmetric SU(N) gauge theory, offering strong evidence supporting Maldacena's conjecture by matching gauge theory results with superstring theory predictions.

Contribution

It sums all leading-order multi-instanton contributions in the large-N limit and demonstrates their geometric and functional correspondence with AdS_5 x S^5 and supergravity calculations.

Findings

Large-N instanton moduli space has AdS_5 x S^5 geometry

Exact agreement with type IIB superstring calculations

Multi-instanton contributions match supergravity propagator convolutions

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.