Integração da anomalia conforme em 6D

Abstract

The evaluation of vacuum effective action (EA) is one of the main purposes in quantum gravity and in particular in the semiclassical approach. One of the most effcient methods is the integration of conformal anomaly (trace anomaly), which is suffcient to provide the quantum field theory basis for such phenomena as evaporation of black holes (Hawking effect) and extended version of Starobinsky inflation. The anomaly-induced EA provides suffcient information about the vacuum quantum effects in the high energy limit. Assuming that in ultraviolet (UV) the original field theory possesses local conformal symmetry, one can derive a closed and compact form of effective action of vacuum. Until recently the process of integration of anomaly in curved space has been completely known only in the two and four-dimensional (D = 2 and D = 4) cases. In the present thesis we report on the details of integrating anomaly in D = 6. The anomaly in six dimensions is given by the local terms which have six derivatives of the metric. We find the explicit form of effective action which is responsible for the anomaly. The result is presented in nonlocal covariant form and also in the local covariant form with two auxiliary scalar fields. It can be shown that the same form with two auxiliary fields holds in higher even dimensions of the space-time.