AdS${}_3$ four-point functions from $\frac{1}{8}$-BPS states

Abstract

We compute four-point functions in the Heavy-Heavy-Light-Light limit involving all possible $\frac{1}{8}$-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 AdS${}_3\times S^3\times {\mathcal{M}}_4$ 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 $\mathcal{N}=(4,4)$ 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 $\frac{1}{4}$-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 AdS${}_3$ involving $\frac{1}{8}$-BPS operators.

arXiv comment38 pages, 3 figures. v2: matches the published version on JHEP; some references added; minor typos corrected

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