Dimensionally continued infinite reduction of couplings

Abstract

The infinite reduction of couplings is a tool to consistently renormalize a wide class of non-renormalizable theories with a reduced, eventually finite, set of independent couplings, and classify the non-renormalizable interactions. Several properties of the reduction of couplings, both in renormalizable and non-renormalizable theories, can be better appreciated working at the regularized level, using the dimensional-regularization technique. We show that, when suitable invertibility conditions are fulfilled, the reduction follows uniquely from the requirement that both the bare and renormalized reduction relations be analytic in ε = D − d, where D and d are the physical and continued spacetime dimensions, respectively. In practice, physically independent interactions are distinguished by relatively non-integer powers of ε. We discuss the main physical and mathematical properties of this criterion for the reduction and compare it with other equivalent criteria. The leading-log approximation is solved explicitly and contains sufficient information for the existence and uniqueness of the reduction to all orders.

Infinite reduction of couplings in non-renormalizable quantum field theory

“…To keep the notation to a minimum, in the rest of the paper I work in the absence of marginal three-leg vertices, since it is straightforward to adapt the arguments to the other case when necessary. More details can be found in [20].…”