The Vilkovisky-DeWitt effective action and its application to Yang-Mills theories

Abstract

In gauge theories both gauge invariance and gauge independence can be achieved by the reparametrization invariant definition of effective actions due to Vilkovisky and its amendment by DeWitt. In Yang-Mills theories we establish the precise connection to the conventional definition to all orders of perturbation theory. An explicit calculation in 2-loop order verifies the necessity of DeWitt's modification in order to preserve renormalization. Some of the new Feynman rules following from the Vilkovisky-DeWitt effective action are made explicit, and gauge independence of the new off-shell vertex functions is checked in the example of the non-abelian gauge field self energy evaluated in 1-loop order in various gauges. The novel definition of the effective action is then applied to spontaneously broken Yang-Mills theories to obtain a gauge independent renormalization group equation. The decoupling threshold of the running gauge coupling constant which is a crucial quantity in grand unified theories is computed to 1-loop accuracy.