Abstract
We derive the connected tree-level part of 4-point holographic correlators in AdS3 × S3 × mathcal{M} (where mathcal{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.
Highlights
Ever since the early days of their study, the approach of Witten diagrams [1] provided an explicit avenue for the calculation of holographic correlators among light single-trace operators and several results were obtained for 4-point correlators in the important example of N = 4 SYM theory [2,3,4,5,6,7]
From quadratic fluctuations around these supergravity solutions it is possible — by using the standard AdS/CFT dictionary — to derive so-called HHLL 4-point correlators with two heavy states corresponding to the geometry and two light states corresponding to the fluctuations
We have studied correlation functions involving two single-trace and two multi-trace light operators obtained from the light limit of HHLL holographic correlators
Summary
The main object of study in this paper is a special class of holographic correlators in the CFT2 dual to type IIB superstring theory on AdS3 × S3 × M, where M can be either T 4 or K3. Than the lower point examples since the method introduced in [7] to deal with bulk-to-bulk propagators will not be sufficient to evaluate them This can be seen by considering the connected tree-diagram given in figure 2a. To have a well-defined semiclassical description it is natural to consider particular coherent-state-like linear combinations of multi-particle states [22, 36, 37] that are dual to a class of asymptotically AdS3×S3 supergravity solutions Since these coherent states are classical supergravity objects, one can expect that they receive contributions only from the tree-level diagrams such as the ones in figure 1b and 2a and that loop diagrams cancel out. The remainder of the connected part of this correlator is the N −2 terms not containing loops (plus higher-order terms in 1/N coming from connected higher-loop diagrams that are not captured by the supergravity approximation)
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