Holographic correlators in AdS$_3$

TL;DR

This work computes four-point functions of dimension-1 scalar single-trace operators in the D1D5 AdS$_3$/CFT$_2$ setup by bypassing problematic Witten diagrams and instead leveraging a small-$b$ limit of heavy-heavy-light-light (HHLL) correlators combined with cross-channel OPE consistency. The authors reconstruct the light-light-light-light (LLLL) correlator from HHLL data, fix ambiguities with Mellin-space contact terms, and extend the result to the full $SU(2)_L\times SU(2)_R$ R-symmetry multiplet, obtaining compact, OPE-consistent expressions in terms of $\eta$-functions $\,\hat{D}$-functions. They also discuss implications for the spectrum of double-trace operators, providing averaged anomalous dimensions via a Lorentzian inversion-type analysis, and outline the path toward a full holographic doubling of the AdS$_3$ correlator program, including potential Minkowski-space OPE data extraction. Overall, the paper delivers the first holographic correlators of single-trace operators in AdS$_3$, with explicit R-symmetry structure and preliminary double-trace anomalous-dimension data, paving the way for more comprehensive AdS$_3$ holographic bootstrap studies.

Abstract

We derive the four-point correlators of scalar operators of dimension one in the supergravity limit of the D1D5 CFT holographically dual to string theory on AdS$_3\times S^3\times \mathcal{M}$, with $\mathcal{M}$ either $T^4$ or $K3$. We avoid the use of Witten diagrams but deduce our result from a limit of the heavy-heavy-light-light correlators computed in arXiv:1705.09250, together with several consistency requirements of the OPE in the various channels. This result represents the first holographic correlators of single-trace operators computed in AdS$_3$.