Holographic 4-point correlators with heavy states

Abstract

Abstract:The AdS/CFT duality maps supersymmetric heavy operators with conformal dimension of the order of the central charge to asymptotically AdS supergravity solutions. We show that by studying the quadratic fluctuations around such backgrounds it is possible to derive the 4-point correlators of two light and two heavy states in the supergravity approximation. We provide an explicit example in the AdS 3 setup relevant for the duality with the D1-D5 CFT. Contrary to previously studied examples, the supergravity correlator derived in this work differs from the result obtained at the CFT orbifold point. Our method bypasses the difficulties of applying the standard Witten's diagrams approach to correlators with operators of large conformal dimension and also avoids some technical steps that have made the computation of dynamical 4-point correlators in the AdS 3 /CFT 2 context unfeasible until now.

Unitary 4-point correlators from classical geometries

“…First we consider the bosonic light operator studied in [19,20] (see (2.5)) which is a superdescendant of the chiral primary operator mentioned above. This implies that the HHLL correlators derived in this paper should satisfy a Ward identity linking them to the correlators computed in [23] (see (2.12)); as a consistency check, when we specify our new supergravity results to the heavy state considered in [23], we show that the Ward identity is satisfied. On the gravity side, the derivation of the HHLL correlators is drastically simplified with respect to [23] because the gravity perturbation dual to the light operator is described by the scalar Laplace equation in six dimensions, while for the case of the CPO one had to deal with a coupled system of a scalar and a 3-form.…”

“…We bypass this issue by exploiting the known smooth geometries dual to the heavy states; then we use the standard AdS/CFT dictionary to calculate the HHLL correlators by studying the quadratic fluctuations of the supergravity field dual to the light operators in the asymptotically AdS geometry describing the heavy operators. This technique was developed [22,23] in several concrete examples in the AdS 3 /CFT 2 context which is of interest for this paper. In particular, these works discussed the case where the light operator is a simple chiral primary operator (see (2.7)): [22] focussed on the case where the heavy state is made out of many copies of the same supergravity mode and found that the 4-point correlator at the gravity point matched precisely the orbifold theory result, suggesting that there is a non-renormalisation theorem for this type of correlators; [23] considered a more complicated heavy operator made out of two types of supergravity modes.…”

“…This technique was developed [22,23] in several concrete examples in the AdS 3 /CFT 2 context which is of interest for this paper. In particular, these works discussed the case where the light operator is a simple chiral primary operator (see (2.7)): [22] focussed on the case where the heavy state is made out of many copies of the same supergravity mode and found that the 4-point correlator at the gravity point matched precisely the orbifold theory result, suggesting that there is a non-renormalisation theorem for this type of correlators; [23] considered a more complicated heavy operator made out of two types of supergravity modes. This second case provides the first explicit example of a dynamical HHLL correlator, where the result in the SCFT strong coupling region is radically different from the one valid at 2 There is a vast literature on holographic four point correlators in the context of the AdS 5 /N = 4 SYM duality; see [18] for a detailed discussion of a modern approach to the problem and references to original papers.…”

“…In this work we generalise the analysis of [23] in several directions. First we consider the bosonic light operator studied in [19,20] (see (2.5)) which is a superdescendant of the chiral primary operator mentioned above.…”

“…One of the results of this paper is an explicit expression for the correlator (1.1) with this type of heavy states, in the supergravity region of the SCFT moduli space. In an alternative approach we focus on a RR ground state that was considered also in [23] and is made out of only the |++ 1 and |00 1 modes. However, we keep the ratio…”