Completeness and consistency of renormalisation group flows

Abstract

We study different renormalisation group flows for scale dependent effective actions, including exact and proper-time renormalisation group flows. These flows have a simple one loop structure. They differ in their dependence on the full field-dependent propagator, which is linear for exact flows. We investigate the inherent approximations of flows with a non-linear dependence on the propagator. We check explicitly that standard perturbation theory is not reproduced. We explain the origin of the discrepancy by providing links to exact flows both in closed expressions and in given approximations. We show that proper-time flows are approximations to Callan-Symanzik flows. Within a background field formalism, we provide a generalised proper-time flow, which is exact. Implications of these findings are discussed.