AdS3 four-point functions from $$ \frac{1}{8} $$-BPS states

Abstract

We compute four-point functions in the Heavy-Heavy-Light-Light limit involving a large family of 1 8-BPS heavy states whose dual supergravity solutions are explicitly known, avoiding the use of Witten diagrams. This is achieved by using the AdS/CFT dictionary of type IIB supergravity on AdS 3 × S 3 × M 4 that maps supersymmetric heavy operators whose conformal dimension is the order of the central charge to explicit asymptotically AdS supergravity solutions. Using the Ward Identities for the generators of the N = (4, 4) superconformal SU(2) Kac-Moody algebra, we can relate all of these four-point functions to each other and to other known four-point functions involving 1 4-BPS heavy states, furnishing non-trivial checks of the computations. Finally, the Ward Identities can be employed to reconstruct the all-light four-point functions, providing the first holographic correlators of single-trace operators computed in AdS 3 involving 1 8-BPS operators.

The Regge limit of AdS3 holographic correlators

“…N b /N is a free parameter and so following [14,15], we can take a perturbative approach and extract the eikonal order by order in N b /N . Such an approach is well-adapted for the calculation of the HHLL correlators 1 and several explicit examples are known [29][30][31][32][33]. We study the OPE decomposition of such correlators in the channel describing the fusion of a heavy and light state, producing an intermediate excited heavy state -this we call the "cross channel".…”

“…The LLLL version of this correlator was derived in [40] and it will be analysed in section 4.3. 6 Here we follow the conventions of [30,32].…”

“…These heavy operators will, for generic values of N b and n = 0, be mixtures of quasi-primary and descendant parts; only in the light limit N b → 1 will they be pure descendants. In the latter case, and for n = 1, a Ward identity relates the correlator of primary operators with that containing two primaries and two descendants [32]. Exploiting the equivalence of the LLLL and HHLL correlators at order µ, the same Ward identity can be used to derive the O(µ) correlator in the (1, 0, 1) heavy state from that in the (1, 0, 0) heavy state:…”

Holographic entanglement entropy and complexity of microstate geometries

“…As briefly mentioned in the previous section, some investigation on the holography of the microstate geometries have been conducted; for example, a set of nice computations of 4-point functions involving the two heavy operators dual to the geometry and two light operators dual to supergravity mode on top on that geometry were computed [44,52,[55][56][57][58][59]. We will now focus on the results of [20], since there the computation on the geometry (2.15) was put forward.…”

Counting superstrata

“…i.e. superstrata, two-point function was studied in [83,87,88]. Most of these works focused on the shallow limit but, in [89], the deep throat limit of the (1, 0, n) superstratum was studied using a WKB technique, and it was found that two-point functions decay as in the BTZ black hole for t √ N 1 N 5 R y , while for t ∼ N 1 N 5 R y large echoes are coming back from the cap.…”