Transformações conformes em seis dimensões. Aplicação à densidade de Euler E(6)

Abstract

Higher-derivative theories and their invariance under conformal transformati ons are powerful tools in Quantum Field Theory in curved spaces. The main purpose of our study is to work towards achievement of a generalization of the four dimensional Paneitz conformal operator to analogous six dimension one (∆6). Achieving a six deri vative conformally invariant operator justifies the choice of working in such dimension as a simpler resource for obtaining it. This operator would be of fundamental account in the integration of the conformal anomaly in sixth order derivatives theories. The strong relation between conformal operators and Euler density has been investigated in D = 2 e D = 4. Euler density term - which 4D version is known as topological Gauss-Bonnet term - was extended to the six dimension. In even dimensions, it is represented by D/2 powers of contracted Riemann and Ricci tensors, each of them carrying D derivatives. The transformation of the third order curvature scalars that arise in the study of the conformal anomaly and Euler density in six dimension was obtained as a first step to our goal of achieving ∆6.