A semi-local holographic minimal model

TL;DR

The work analyzes the large-N limit of the W_N minimal model and proposes a complete single-trace spectrum consisting of scalar towers phi_n, tilde phi_n, omega_n, plus an infinite set of approximately conserved higher-spin currents j_n^(s). It advocates a semi-local holographic dual on AdS3 x S1, with a circle of Vasiliev theories at each S1 point interacting only via boundary conditions on a shared massive scalar, thereby preserving a single high-spin tower. The authors derive current non-conservation relations from CFT data, identify an infinite family of hidden symmetries, and provide partition-function checks showing consistency between the CFT and bulk descriptions. They discuss finite-N/k truncations, potential stringy/topological interpretations, and broader implications for holography with semi-local bulk dynamics.

Abstract

We present a conjecture on the complete spectrum of single-trace operators in the infinite N limit of W(N) minimal model and evidences for the conjecture. We further propose that the holographic dual of W(N) minimal model in the 't Hooft limit is an unusual "semi-local" higher spin gauge theory on AdS3 x S^1. At each point on the S^1 lives a copy of three-dimensional Vasiliev theory, that contains an infinite tower of higher spin gauge fields coupled to a single massive complex scalar propagating in AdS3. The Vasiliev theories at different points on the S^1 are correlated only through the AdS3 boundary conditions on the massive scalars. All but one single tower of higher spin symmetries are broken by the boundary conditions.