Abstract
We study a simple class of correlators with two heavy and two light operators both in the D1D5 CFT and in the dual AdS$_3 \times S^3 \times T^4$ description. On the CFT side we focus on the free orbifold point and discuss how these correlators decompose in terms of conformal blocks, showing that they are determined by protected quantities. On the gravity side, the heavy states are described by regular, asymptotically AdS$_3 \times S^3 \times T^4$ solutions and the correlators are obtained by studying the wave equation in these backgrounds. We find that the CFT and the gravity results agree and that, even in the large central charge limit, these correlators do not have (Euclidean) spurious singularities. We suggest that this is indeed a general feature of the heavy-light correlators in unitary CFTs, which can be relevant for understanding how information is encoded in black hole microstates.
Highlights
Probe these states is to calculate the holographic 1-point functions of the different chiral primary operators
We study a simple class of correlators with two heavy and two light operators both in the D1D5 CFT and in the dual AdS3 × S3 × T 4 description
Our approach is based on very standard techniques: on the CFT side we need to calculate a 4-point function with two heavy and two light operators, while on the bulk side we study the wave equation of a light field in the dual non-trivial geometry
Summary
We discuss some simple examples of four-point correlators in the D1D5 CFT. In particular we are interested in correlators with two heavy (OH ) operators, which have conformal dimension of order c, and two light (OL) operators, which have conformal dimension of order one. The light operators we use are chiral primaries both in the left and in the right sector of the CFT. Instead the heavy operators are in the Ramond-Ramond sector of the CFT, but are related to chiral primaries by a chiral algebra transformation that acts only on the left sector ( they generically preserve half of the CFT supercharges). Second we work at the free orbifold point of the CFT moduli space, where the theory, which has central charge c = 6N , is described by a collection of N copies of free fields (we call each such copy a “strand” of length 1). The correlators we consider are relevant both for the (T 4)N /SN and (K3)N /SN CFTs
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