Holographic correlators in AdS${}_3$ without Witten diagrams

Abstract

We present a formula for the holographic 4-point correlators in AdS${}_3\times S^3$ involving four single-trace operators of dimension $k,k,l,l$. As an input we use the supergravity results for the Heavy-Heavy-Light-Light correlators that can be derived by studying the linear fluctuations around known asymptotically AdS${}_3\times S^3$ geometries. When the operators of dimension $k$ and $l$ are in the same multiplet there are contributions due to the exchange of single-trace operators in the $t$ and $u$ channels, which are not captured by the approach mentioned above. However by rewriting the $s$-channel results in Mellin space we obtain a compact expression for the $s$-channel contribution that makes it possible to conjecture a formula for the complete result. We discuss some consistency checks that our proposal meets.

14 pages. v2: minor corrections and references updated; v3: 18 pages, JHEP version

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