Holographic correlators with multi-particle states

We derive the connected tree-level part of 4-point holographic correlators in AdS(3) x S-3 x M (where M is T-4 or K3) involving two multi-trace and two single-trace operators. These connected correlators are obtained by studying a heavy-heavy-light-light correlation function in the formal limit where the heavy operators become light. These results provide a window into higher-point holographic correlators of single-particle operators. We find that the correlators involving multi-trace operators are compactly written in terms of Bloch-Wigner-Ramakrishnan functions - particular linear combinations of higher-order polylogarithm functions. Several consistency checks of the derived expressions are performed in various OPE channels. We also extract the anomalous dimensions and 3-point couplings of the non-BPS double-trace operators of lowest twist at order 1/c and find some positive anomalous dimensions at spin zero and two in the K3 case.

Automated summary

The connected tree-level part of 4-point holographic correlators in AdS(3) x S-3 x M involving multi-trace and single-trace operators were derived. These correlators were found to be compactly written in terms of Bloch-Wigner-Ramakrishnan functions for multi-trace operators. Consistency checks were performed on the derived expressions and anomalous dimensions of non-BPS double-trace operators were extracted.