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

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

1994-09-14

arxiv.org/abs/hep-th/9409081v1

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, report REF.TUW 94-17

Scientific paper

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.

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