Instantons in supersymmetric Yang-Mills and D-instantons in IIB superstring theory

TL;DR

This work provides a compelling cross-check of the AdS/Yang–Mills correspondence by matching one-instanton effects in ${\cal N}=4$ SYM with D-instanton contributions in type IIB string theory on ${\rm AdS}_5 \times S^5$. The authors compute explicit YM instanton correlators that soak the 16 gaugino zero modes and show that their leading nonperturbative structures align with the corresponding D-instanton amplitudes arising from ${\cal R}^4$-type and ${\Lambda}^{16}$ terms in the IIB effective action, including the correct exponential suppressions and moduli-space dependences. A detailed analysis of the D-instanton solution in the AdS background reveals how the YM instanton scale size maps to the D-instanton position in the extra dimensions, reinforcing the interpretation of the YM moduli space as part of the bulk geometry. The results support the Maldacena conjecture and point to rich nonperturbative structures, with clear avenues for extension to larger gauge groups and the large-$N_c$ limit, where quantitative matching should be sharpened.

Abstract

The one-instanton contributions to various correlation functions of supercurrents in four-dimensional N=4 supersymmetric SU(2) Yang-Mills theory are evaluated to the lowest order in perturbation theory.Expressions of the same form are obtained from the leading effects of a single D-instanton extracted from the IIB superstring effective action around the AdS5*S5 background. This is in line with the suggested AdS/Yang-Mills correspondence. The relation between Yang--Mills instantons and D-instantons is further confirmed by the explicit form of the classical D-instanton solution in the AdS5*S5 background and its associated supermultiplet of zero modes. Speculations are made concerning instanton effects in the large-N_c limit of the SU(N_c) Yang-Mills theory.