An AdS_3 Dual for Minimal Model CFTs

TL;DR

This work proposes a concrete AdS_3/higher-spin duality for a continuous family of 2D ${ m W}_N$ minimal models in the large-N 't Hooft limit, linking them to a higher-spin theory on AdS_3 with two complex scalar matter fields. The bulk theory reproduces the CFT spectrum via 1-loop partition functions and mirrors the RG flows through double-trace deformations and quantization choices for the scalars, aligning with DS-reduced ${ m W}_N$ boundary symmetry. The results provide nontrivial evidence for a gravity-like dual in a non-Einstein, higher-spin regime and open avenues for deriving the dual from a Chern-Simons/Drinfeld-Sokolov framework. Overall, the paper extends the Klebanov–Polyakov paradigm to 3D, offering a controllable setting to study gravity emergence and higher-spin holography in two dimensions.

Abstract

We propose a duality between the 2d W_N minimal models in the large N 't Hooft limit, and a family of higher spin theories on AdS_3. The 2d CFTs can be described as WZW coset models, and include, for N=2, the usual Virasoro unitary series. The dual bulk theory contains, in addition to the massless higher spin fields, two complex scalars (of equal mass). The mass is directly related to the 't Hooft coupling constant of the dual CFT. We give convincing evidence that the spectra of the two theories match precisely for all values of the 't Hooft coupling. We also show that the RG flows in the 2d CFT agree exactly with the usual AdS/CFT prediction of the gravity theory. Our proposal is in many ways analogous to the Klebanov-Polyakov conjecture for an AdS_4 dual for the singlet sector of large N vector models.