D-Instanton in AdS_5 and Instanton in SYM_4

TL;DR

This paper extends the Banks–Green/Witten proposal that D-instantons in $AdS_5\times S^5$ correspond to YM instantons on the ${\cal N}=4$ SYM boundary. By constructing a D-instanton solution smeared over $S^5$ and a half-BPS ansatz that relates the dilaton/axion to the RR fields, the authors show consistent matching of instanton actions and SUSY between the bulk and boundary, and they identify a holographic map between bulk moduli and YM instanton data, including the crucial relation $L=1/U$. They then propose a general conjecture: any SUGRA solution satisfying the ansatz corresponds to an (anti-)self-dual YM configuration, and they derive correlator identities from regular, non-singular solutions, illustrating how boundary operators like ${\cal O}_{\phi}$ and ${\cal O}_{\chi}$ couple to bulk fluctuations. Collectively, these results reinforce a broader, background-dependent AdS/CFT dictionary for branes and instantons, and they illustrate how D-instanton backgrounds can induce structured identities among SYM correlators. The work provides a concrete framework to study non-perturbative objects in the boundary theory via bulk D-brane configurations and opens pathways to compute an infinite class of SYM correlators from regular SUGRA solutions.

Abstract

Following the observation of Banks and Green that the D-instantons in AdS_5 correspond to the instantons in 4-dimensional supersymmetric Yang-Mills theory, we study in more detail this correspondence for individual instantons. The supergravity solution for a D-instanton in AdS_5 is found using the ansatz used previously for D-instantons in flat space. We check that the actions and supersymmetries match between the D-instanton solution and the Yang-Mills instanton. Generalizing this result, we propose that any supergravity solution satisfying the ansatz corresponds to a (anti-)self-dual Yang-Mills configuration. Using this ansatz a family of identities for correlation functions in the supersymmetric Yang-Mills theory are derived.