Gravitational and gauge couplings in Chern-Simons fractional spin gravity

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.

Published in JHEP. 32 pages, 3 figures

References in corpus (5)

• Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
• Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity
• Quantum W-symmetry in AdS_3
• Three-dimensional supergravity reloaded
• Covariant Structure Constants for Deformed Oscillator Algebra

Cited by in corpus (2)

• An Action for Matter Coupled Higher Spin Gravity in Three Dimensions
• Action principles for higher and fractional spin gravities