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

Abstract

Abstract We compute four-point functions in the Heavy-Heavy-Light-Light limit involving a large family of 1 8 $$ \frac{1}{8} $$ -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 AdS3 × S 3 × ℳ4 that maps supersymmetric heavy operators whose conformal dimension is the order of the central charge to explicit asymp-totically AdS supergravity solutions. Using the Ward Identities for the generators of the N = 4 4 $$ \mathcal{N}=\left(4,4\right) $$ superconformalSU(2)Kac-Moodyalgebra,wecanrelateallofthesefour-point functions to each other and to other known four-point functions involving 1 4 $$ \frac{1}{4} $$ -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 AdS3 involving 1 8 $$ \frac{1}{8} $$ -BPS operators.

Keywords

• AdS-CFT Correspondence
• Black Holes in String Theory
• Conformal Field Theory