Holographic correlators in \( \mathrm{AdS}_{3} \) without Witten diagrams

DOI10.1007/JHEP09(2019)030zbMATH Open1423.81158arXiv1905.12314OpenAlexW3122630246WikidataQ127300062 ScholiaQ127300062MaRDI QIDQ2332196

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Publication date: 1 November 2019

Published in: (Search for Journal in Brave)

Abstract: We present a formula for the holographic 4-point correlators in AdS${}_{3}imes{S}^3$ 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${}_{3}imes{S}^3$ 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.

Full work available at URL: https://arxiv.org/abs/1905.12314

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