Flow Equations and BRS Invariance for Yang-Mills Theories

Abstract

Flow equations describe the evolution of the effective action ${\Gamma }_k$ in the process of varying an infrared cutoff $k$. The presence of the infrared cutoff explicitly breaks gauge and hence BRS invariance. We derive modified Slavnov-Taylor identities, which are valid for nonvanishing $k$. They guarantee the BRS invariance of ${\Gamma }_k$ for $k\to 0$, and hence allow the study of non-abelian gauge theories by integrating the flow equations. Within a perturbative expansion of ${\Gamma }_k$, we derive an equation for a $k$ dependent mass term for the gauge fields implied by the modified Slavnov-Taylor identities.

Comments: 10 pages, HD-THEP-94-02 (References and example added; version to appear in Phys. Lett. B)