Four-point correlators with BPS bound states in AdS₃ and AdS₅

We consider heavy-heavy-light-light (HHLL) correlators in AdS/CFT, focussing on the D1D5 CFT₂ and the N= 4 super Yang-Mills theory. Out of the lightest $1/2$-BPS operator in the spectrum, O, we construct a particular heavy operator OH given by a coherent superposition of multi-particle operators Oⁿ, and study the HHLL correlator. When n is of order of the central charge, we show that the bulk equation that computes our boundary HHLL correlators is always a Heun equation. By assuming that the form of the correlator can be continued to the regime where n is O(1), we first reproduce the known single-particle four-point correlators for $n=1$ and then predict new results for the multi-particle correlators Oⁿ Oⁿ O O. Explicit expressions can be written entirely in terms of n-loop ladder integrals and their derivatives, and we provide them for $n=2$ and $n=3$ both in position and in Mellin space. Focussing on the AdS₅ case, we study the OPE expansion of these multi-particle correlators and show that several consistency relations with known CFT data are non-trivially satisfied. Finally, we extract new CFT data for double and triple-particle long operators.