On the conformal properties of topological terms in even dimensions

TL;DR

This paper investigates the conformal properties of topological gravitational terms in even dimensions, revealing invariance features and deriving operators like the Paneitz operator, with conjectures on higher-dimensional structures.

Contribution

It provides a covariant derivation of the Paneitz operator in four dimensions and proposes conjectures on conformal properties of topological terms in higher even dimensions.

Findings

Integrands of topological terms become conformally invariant when adjusted for dimension and scalar multiplication.

A simple covariant derivation of the Paneitz operator in four dimensions is presented.

Two conjectures on conformal properties of topological structures in even dimensions are formulated.

Abstract

Conformal properties of the topological gravitational terms in $D=2$, $D=4$ and $D=6$ are discussed. It is shown that in the last two cases the integrands of these terms, when being settled into the dimension $D-1$ and multiplied by a scalar, become conformal invariant. Furthermore we present a simple covariant derivation of the Paneitz operator in $D=4$ and formulate two general conjectures concerning the conformal properties of topological structures in even dimensions.