Unfolding Conformal Geometry

Abstract

Conformal geometry is studied using the unfolded formulation à la Vasiliev. Analyzing the first-order consistency of the unfolded equations, we identify the content of zero-forms as the spin-two off-shell Fradkin-Tseytlin module of $\mathfrak{so}(2,d)$. We sketch the nonlinear structure of the equations and explain how Weyl invariant densities, which Type-B Weyl anomaly consist of, could be systematically computed within the unfolded formulation. The unfolded equation for conformal geometry is also shown to be reduced to various on-shell gravitational systems by requiring additional algebraic constraints.

45 pages

References in corpus (26)

• The Holographic Weyl anomaly
• Nonlinear Equations for Symmetric Massless Higher Spin Fields in $(A)d{S}_d$
• Twenty Years of the Weyl Anomaly
• Geometric Classification of Conformal Anomalies in Arbitrary Dimensions
• Geometric Formulation for Partially Massless Fields
• Unfolding Mixed-Symmetry Fields in AdS and the BMV Conjecture: I. General Formalism
• Higher order singletons, partially massless fields and their boundary values in the ambient approach
• Frame-Like Action and Unfolded Formulation for Massive Higher-Spin Fields
• Parent field theory and unfolding in BRST first-quantized terms
• Bosonic conformal higher--spin fields of any symmetry
• Partition function of free conformal higher spin theory
• Conformally Covariant Differential Operators: Properties and Applications
• Unfolding Mixed-Symmetry Fields in AdS and the BMV Conjecture: II. Oscillator Realization
• Algebraic Classification of Weyl Anomalies in Arbitrary Dimensions
• General solutions of the Wess-Zumino consistency condition for the Weyl anomalies
• Weyl gravity as general relativity
• First order parent formulation for generic gauge field theories
• A classification of local Weyl invariants in D=8
• Conformal Field Theory in Conformal Space
• Conformal geometry and (super)conformal higher-spin gauge theories
• A Weyl-covariant tensor calculus
• Conformal gravity does not predict flat galaxy rotation curves
• On unfolded off-shell formulation for higher-spin theory
• Conformal Higher-Spin Gravity: Linearized Spectrum = Symmetry Algebra
• BRST structure for the mixed Weyl-diffeomorphism residual symmetry
• AdS Chern-Simons Gravity induces Conformal Gravity

Cited by in corpus (1)

• Presymplectic BV-AKSZ formulation of Conformal Gravity