Holographic correlators with multi-particle states

Abstract

We derive the connected tree-level part of 4-point holographic correlators in AdS3 × S3 × $$ \mathcal{M} $$ M (where $$ \mathcal{M} $$ M is T4 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.

Rebooting quarter-BPS operators in $\mathcal{N}=4$ Super Yang-Mills

“…in a holographic computation, that such a basis is not enough and needs to be supplemented with more general functions [48]. We hope to be able to clarify this point in the future.…”

AdS$_3$ holography for non-BPS geometries

“…The information about such anomalous dimension is in principle contained in the four-point correlator involving the CPO O 1 2 , 1 2 , which has been computed in [44]. In the AdS 3 context anomalous dimensions of two-particle operators have already been derived in [45,46]. However finding a precise relation between CFT anomalous dimensions and our non-BPS supergravity solutions is technically challenging.…”

Selected Topics in Analytic Conformal Bootstrap: A Guided Journey

“…This paves the way for a future bootstrap strategy. On the other hand, in AdS 3 it was shown in [247] that the approach of [244,245] can be extended to compute tree-level four-point functions with two single-trace operators and two multi-trace operators. A particularly interesting feature pointed out in [247] is that the tree-level multi-trace correlators necessarily involve building block functions in position space which are generalizations of the D-functions.…”