Unfolding Conformal Geometry

TL;DR

This paper applies the unfolded formulation to conformal geometry, identifying key modules and outlining how to compute Weyl anomalies and reduce to gravitational systems, advancing the theoretical understanding of conformal structures.

Contribution

It introduces an unfolded formulation approach to conformal geometry, revealing the structure of zero-forms and proposing a method to compute Weyl anomalies systematically.

Findings

Identifies the zero-forms as the spin-two off-shell Fradkin-Tseytlin module.

Sketches the nonlinear structure of unfolded conformal equations.

Shows reduction to on-shell gravitational systems with algebraic constraints.

Abstract

Conformal geometry is studied using the unfolded formulation \`a 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.