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

O. Moritsch·M. Schweda·T. Sommer·L. Tataru·H. Zerrouki
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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 $δ$ 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.

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O. Moritsch, M. Schweda, T. Sommer, L. Tataru, H. Zerrouki. 1994-09-14. BRST cohomology of Yang-Mills gauge fields in the presence of gravity in Ashtekar variables. https://arxiv.org/abs/hep-th/9409081

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