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

Research paper by O. Moritsch, M. Schweda, T. Sommer, L. Tataru, H. Zerrouki

Indexed on: 14 Sep '94Published on: 14 Sep '94Published in: High Energy Physics - Theory

#### Abstract

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 $\delta$ 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.