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arXiv · hep-th/9206097

The regularized BRST Jacobian of pure Yang-Mills theory

F. De Jonghe·R. Siebelink·W. Troost·S. Vandoren·P. van Nieuwenhuizen·A. Van Proeyen
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Abstract

The Jacobian for infinitesimal BRST transformations of path integrals for pure Yang-Mills theory, viewed as a matrix $\unity +ΔJ$ in the space of Yang-Mills fields and (anti)ghosts, contains off-diagonal terms. Naively, the trace of $ΔJ$ vanishes, being proportional to the trace of the structure constants. However, the consistent regulator $\cR$, constructed from a general method, also contains off-diagonal terms. An explicit computation demonstrates that the regularized Jacobian $Tr\ ΔJ\exp -\cR /M^2$ for $M^2\rightarrow \infty $ is the variation of a local counterterm, which we give. This is a direct proof at the level of path integrals that there is no BRST anomaly.

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F. De Jonghe, R. Siebelink, W. Troost, S. Vandoren, P. van Nieuwenhuizen, A. Van Proeyen. 1992-06-25. The regularized BRST Jacobian of pure Yang-Mills theory. https://doi.org/10.1016/0370-2693(92)91231-w

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