Higher Spins, Holography and Exotic Matter

TL;DR

This paper explores a new perspective on higher-spin holography, revealing how 4D higher-spin gravity and 3D conformal matter fields emerge as reductions of a parent non-commutative sigma model with a fractional-spin algebra.

Contribution

It introduces a novel framework connecting higher-spin gravity, conformal matter, and exotic fractional-spin extensions through a unifying non-commutative sigma model.

Findings

Identification of a non-commutative AKSZ sigma model as a parent structure.

Description of 4D fractional-spin gravity with exotic matter.

Connection between higher-spin theories and conformal matter fields.

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.