The regularized BRST Jacobian of pure Yang-Mills theory

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 $\Delta J$ 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 $M^2\to \infty$ 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.

12 pages, latex, CERN-TH.6541/92, KUL-TF-92/24

Cited by in corpus (8)

• Antibracket, Antifields and Gauge-Theory Quantization
• Loop quantum gravity: an outside view
• Simplifications in Lagrangian BV quantization exemplified by the anomalies of chiral $W_3$ gravity
• Master Equations for Extended Lagrangian BRST Symmetries
• The BPHZ renormalised BV master equation and Two-loop Anomalies in Chiral Gravities
• BRST Gauge Fixing and Regularization
• Schwinger--Dyson BRST symmetry and the Batalin--Vilkovisky Lagrangian Quantisation of Gauge Theories with Open or Reducible Gauge Algebras
• Batalin-Vilkoviski master equation and absence of anomalies in string field theory