Gravitational and gauge couplings in Chern-Simons fractional spin gravity

TL;DR

This paper establishes conditions for supertrace consistency in a three-dimensional Chern--Simons higher spin gravity model with fractional spin fields, analyzing gauge couplings and algebraic structures.

Contribution

It introduces a ground state projector ensuring supertrace consistency and explores the relation between gravitational and gauge couplings in fractional spin higher spin theories.

Findings

Supertrace consistency condition derived and verified.

Relation between gravitational and gauge couplings established.

Finite and infinite dimensional gauge algebras identified for different fractional spins.

Abstract

We provide a necessary and sufficient condition for the consistency of the supertrace, through the existence of a certain ground state projector. We build this projector and check its properties to the first two orders in the number operator and to all orders in the deformation parameter. We then find the relation between the gravitational and internal gauge couplings in the resulting unified three-dimensional Chern--Simons theory for Blencowe--Vasiliev higher spin gravity coupled to fractional spin fields and internal gauge potentials. We also examine the model for integer or half-integer fractional spins, where infinite dimensional ideals arise and decouple, leaving finite dimensional gauge algebras $gl(2l+1)$ or $gl(l|l+1)$ and various real forms thereof.