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arXiv · 1905.12314

Holographic correlators in AdS$_3$ without Witten diagrams

Stefano Giusto·Rodolfo Russo·Alexander Tyukov·Congkao Wen
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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.

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Stefano Giusto, Rodolfo Russo, Alexander Tyukov, Congkao Wen. 2019-05-29. Holographic correlators in AdS$_3$ without Witten diagrams. https://doi.org/10.1007/jhep09(2019)030

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