Unravelling AdS$_3$/CFT$_2$ near the boundary

TL;DR

This paper computes correlation functions of spectrally-flowed vertex operators in bosonic string theory on AdS3, showing exact agreement with dual CFT predictions near the boundary, thus providing strong evidence for the AdS3/CFT2 duality.

Contribution

It introduces a method to compute boundary correlation functions in AdS3 string theory that precisely match dual CFT results, supporting the holographic duality.

Findings

Correlation functions match dual CFT predictions at all orders.

Near-boundary restriction simplifies the path integral.

Provides evidence for the AdS3/CFT2 duality.

Abstract

We study correlation functions of spectrally-flowed vertex operators in bosonic string theory on $\text{AdS}_3\times X$ in the path integral formalism. By restricting the path integral to only include worldsheets which live near the asymptotic boundary, we compute correlation functions of spectrally-flowed vertex operators and find a precise agreement with the perturbative correlators in the recently-proposed dual CFT at all orders in conformal perturbation theory. We thus provide highly nontrivial evidence for the bulk/boundary duality.