On the equivalence between Implicit Regularization and Constrained Differential Renormalization

TL;DR

This paper demonstrates the equivalence between Constrained Differential Renormalization and Implicit Regularization at one-loop order, showing they can be mapped onto each other and are reliable, symmetry-preserving regularization methods.

Contribution

It establishes the one-loop equivalence between CDR and IR, bridging their configuration and momentum space frameworks.

Findings

CDR and IR are equivalent at one-loop order.

Configuration space rules of CDR map to momentum space procedures of IR.

Both methods preserve gauge and supersymmetry in perturbative calculations.

Abstract

Constrained Differential Renormalization (CDR) and the constrained version of Implicit Regularization (IR) are two regularization independent techniques that do not rely on dimensional continuation of the space-time. These two methods which have rather distinct basis have been successfully applied to several calculations which show that they can be trusted as practical, symmetry invariant frameworks (gauge and supersymmetry included) in perturbative computations even beyond one-loop order. In this paper, we show the equivalence between these two methods at one-loop order. We show that the configuration space rules of CDR can be mapped into the momentum space procedures of Implicit Regularization, the major principle behind this equivalence being the extension of the properties of regular distributions to the regularized ones.