Holographic correlators in AdS$_3$ without Witten diagrams

Understand

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.