Toward Higher Spin dS3/CFT2

TL;DR

The paper investigates higher-spin gravity in de Sitter 3D and derives its asymptotic symmetry group, showing it forms a complexified W_N algebra with an imaginary central charge, explicitly demonstrated for the spin-3 case via a SL(3,C) Chern-Simons formulation. It reviews how W_N arises in AdS3/CFT2 through diagonal WZW cosets and uses this structure to motivate a de Sitter counterpart. A conjecture is proposed that the dS3/CFT2 dual is a non-unitary, Euclidean WZW coset with complex levels, yielding an imaginary central charge and complex operator dimensions, in a large-N, large-γ limit. The work outlines the necessary consistency checks and highlights open issues, including the precise CFT realization and the bulk/boundary dictionary in the de Sitter context.

Abstract

I take steps toward the construction of a CFT dual to Vasiliev's higher spin gravity in three dimensional de Sitter space. There are two main claims. The first is that higher spin de Sitter symmetries are related to extended Virasoro symmetries, as in AdS; this is verified explicitly for the case of W_3 asymptotic symmetry. The associated chiral algebra has imaginary central charge. The second (conjectural) claim, inspired by work of Gaberdiel and Gopakumar in AdS_3/CFT_2, is that an appropriate CFT can be identified as an exotic non-unitary WZW coset model at complex level.