Holographic correlators with multi-particle states

TL;DR

This paper derives explicit forms of 4-point holographic correlators involving multi-trace operators in AdS$_3$ backgrounds, revealing their structure in terms of special functions and providing insights into higher-point correlators and operator dimensions.

Contribution

It presents the first explicit computation of connected tree-level 4-point correlators with multi-trace operators in AdS$_3$, expressed via Bloch-Wigner-Ramakrishnan functions, and analyzes their OPE properties.

Findings

Correlators expressed in terms of special polylogarithm functions.

Extraction of anomalous dimensions and 3-point couplings for double-trace operators.

Positive anomalous dimensions found for certain spins in the K3 case.

Abstract

We derive the connected tree-level part of 4-point holographic correlators in AdS$_3\times S^3\times \mathcal{M}$ (where ${\cal M}$ 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.