Reconstruct the full supersymmetric four-point correlator

Determine the contact-term contribution \(\mathbf{B}^{I_1 I_2 I_3 I_4}\) needed to remove the AdS5 contact-diagram ambiguities and fully reconstruct the \(\mathcal{N}=1\) supersymmetric four-point correlator from its exchange residues.

Background

The $\mathcal{N}=1$ super-Yang–Mills four-point super-correlator is fixed in the paper only through its double residues in the $s$- and $t$-channels. An undetermined term $\mathbf{B}^{I_1 I_2 I_3 I_4}$ has vanishing double residues in those channels but may contain single-channel poles and contact contributions. Fixing this term is therefore necessary for a complete correlator rather than merely its exchange part.