Higher Spins, Holography and Exotic Matter

TL;DR

This work develops a unified, top-down approach to higher-spin holography by embedding 4D Vasiliev-like higher-spin gravity and a 3D coloured conformal HS theory within a single noncommutative Frobenius-Chern-Simons/AKSZ parent model. The key innovation is extending the fibre algebra to a fractional-spin algebra ${oldsymbol{ ext FS}}$ so that different consistent reductions yield, on one hand, 4D higher-spin gravity and, on the other hand, a 3D CHSG with coloured conformal matter coupled to topological HS and colour gauge fields; an intermediate 4D fractional-spin gravity describes coupling to exotic coloured singletons. The analysis shows how boundary currents and conformal data arise from boundary invariants like a generalized second Chern class, and how the colour sector emerges as a dynamical, nonlocal endomorphism algebra tied to the fractional-spin extension. The framework offers a coherent, nonlocal, AKSZ-based route to HS holography and motivates exploring fractional-spin matter as a potential avenue for novel bulk matter phenomenology and holographic dualities.

Abstract

We review a new perspective on higher-spin holography, whereby Vasiliev's 4D higher-spin gravity emerges together with a 3D counterpart, consisting of coloured conformal matter fields coupled to topological conformal higher-spin and colour gauge fields, as two distinct reductions, characterised by dual structure groups, of a common parent model. The latter is given by a non-commutative AKSZ sigma model consisting on-shell of a flat superconnection valued in a fractional-spin extension of Fradkin-Vasiliev's higher-spin algebra. In particular, we highlight an intermediate 4D reduction, referred to fractional-spin gravity, consisting of exotic matter, in the form of coloured singletons, coupled to higher-spin and colour gauge fields.