Eur. Phys. J. Plus (2016) 131: 164
https://doi.org/10.1140/epjp/i2016-16164-9

Regular Article

On the conformal properties of topological terms in even dimensions

¹ Departamento de Física, ICE, Universidade Federal de Juiz de Fora, Campus Universitário - Juiz de Fora, 36036-330, MG, Brazil
² Tomsk State Pedagogical University and Tomsk State University, 634041, Tomsk, Russia
³ Instituto Federal de Educação, Ciência e Tecnologia do Sudeste de Minas Gerais, IF Sudeste MG - Juiz de Fora, 36080-001, MG, Brazil

^* e-mail: fabricio.ferreira@ifsudestemg.edu.br

Received: 14 April 2016
Accepted: 23 April 2016
Published online: 24 May 2016

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.