Minimal Model Holography for SO(2N)

TL;DR

This work demonstrates a precise holographic duality between the large-$N$ 't Hooft limit of the WD$_N$ minimal models and a higher-spin gravity theory on AdS$_3$ truncated to even spins $s=2,4,6,\ldots$, coupled to two real scalars with masses fixed by the algebra. By computing the bulk 1-loop partition function and the WD$_N$ CFT partition function in the large-$N$ limit, and carefully removing decoupled (null) states, the authors show exact matching, reinforcing the AdS$_3$/CFT$_2$ duality for this family. The analysis leverages the hs$[\lambda]$ higher-spin algebra, Weyl-denominator techniques, and Schur-function bases to organize branching functions and characters, revealing that the physically relevant states are encoded by finite Young tableaux with transposed shapes. The results point to a natural bulk realization via a Chern–Simons theory based on hs$[\lambda]$ (likely restricted to even spins) with two real scalars, and they open avenues for exploring similar dualities in related W-algebra families.

Abstract

A duality between the large N 't Hooft limit of the WD_N minimal model CFTs and a higher spin gravity theory on AdS3 is proposed. The gravity theory has massless spin fields of all even spins s=2,4,6,..., as well as two real scalar fields whose mass is determined by the 't Hooft parameter of the CFT. We show that, to leading order in the large N limit, the 1-loop partition function of the higher spin theory matches precisely with the CFT partition function.