Dimensionally continued infinite reduction of couplings

TL;DR

This paper explores a method for reducing couplings in quantum field theories through dimensional regularization, ensuring unique and consistent renormalization of non-renormalizable interactions by analyzing analyticity in the continued spacetime dimension.

Contribution

It introduces a dimensionally continued approach to infinite coupling reduction, establishing conditions for uniqueness and physical relevance of the reduced interactions.

Findings

Reduction follows uniquely from analyticity in epsilon under invertibility conditions.

Physically independent interactions are characterized by non-integer powers of epsilon.

Explicit solution of leading-log approximation confirms existence and uniqueness of the reduction.

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 epsilon=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 epsilon. 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.