Non-Minimal Higher-Spin DS4/CFT3

TL;DR

We address the problem of extending the dS$_4$/CFT$_3$ holographic dictionary to non-minimal, parity-violating higher-spin Vasiliev theories and their dual Chern-Simons-matter field theories. Our approach relies on analytic continuation from AdS$_4$ to dS$_4$ and a careful mapping of boundary conditions for the bulk scalar to the statistics of boundary matter, yielding a dictionary between bulk phase $\theta_0$, coupling $g_{dS}^2$, and boundary data $N$, $\lambda$. The key contributions are (i) a concrete proposal for dS$_4$/CFT$_3$ dual pairs involving $U(N)_k$ and $Sp(N)_k$ Chern-Simons theories with wrong-statistics matter, (ii) a detailed AdS$_4$–to–dS$_4$ analytic continuation of higher-spin fields and correlators, and (iii) a unifying framework that connects minimal and non-minimal higher-spin theories and extends known dualities to the de Sitter setting. This work deepens the understanding of higher-spin holography in de Sitter space and provides a pathway to explore parity-violating bulk theories and their boundary CFTs in cosmological contexts.

Abstract

We conjecture that the level k U(N) Chern-Simons theory coupled to free anticommuting scalar matter in the fundamental is dual to non-minmal higher-spin Vasiliev gravity in dS4 with parity-violating phase \theta0 = πN/2k and Neumann boundary conditions for the scalar. Related conjectures are made for fundamental commuting spinor matter and critical theories. This generalizes a recent conjecture relating the minimal Type A Vasiliev theory in dS4 to the Sp(N) model with fundamental real anti-commuting scalars.