Interpret and normalize correlators for p = −1 (D-instanton) case

Determine the correct physical interpretation and develop a reliable normalization prescription for n-point functions produced by the auxiliary CFT integration prescription when p = −1, where the worldvolume is a point and the resulting correlators reduce to numerical values without position dependence.

Background

The proposed prescription integrates CFT_D correlators over η auxiliary directions to obtain SYM_{p+1} correlators. For p = −1, the brane worldvolume is a point, so the correlators lose position dependence and become pure numbers.

The authors note that the interpretation of these numbers is unclear, particularly because a reliable method to fix the normalization of holographic correlators in this setup is lacking, leading them to restrict subsequent analysis to p ≥ 0.