BRST cohomology of Yang-Mills gauge fields in the presence of gravity in Ashtekar variables

The BRST transformations for the Yang-Mills gauge fields in the presence of gravity described by Ashtekar variables are obtained by using the so-called Maurer-Cartan horizontality conditions. The BRST cohomology group expressed by the Wess-Zumino consistency condition is solved with the help of an operator δ introduced by S.P. Sorella which in our case has a very simple form and generates, together with the differential d and the BRST operator s, a simpler algebra than in the pure Yang-Mills theory. In this way we shall find the Yang-Mills Lagrangians, the Chern-Simons terms and the gauge anomalies. Work supported in part by the “Fonds zur Förderung der Wissenschaftlichen Forschung” under Contract Grant Number P9116-PHY. Work supported in part by the “Fonds zur Förderung der Wissenschaftlichen Forschung” under Contract Grant Number P10268-PHY. Supported by the “Österreichisches Bundesministerium für Wissenschaft und Forschung”. Permanent address Dept. Theor. Phys., University of Cluj, Romania. Work supported in part by the “Fonds zur Förderung der Wissenschaftlichen Forschung” under Contract Grant Number P10268-PHY.