Momentum routing invariance in Feynman diagrams and quantum symmetry breakings

TL;DR

This paper explores how momentum routing invariance (MRI) in Feynman diagrams is crucial for maintaining quantum symmetries like gauge invariance and supersymmetry, and discusses its role in anomalies and renormalization.

Contribution

It demonstrates that MRI is both necessary and sufficient for preserving abelian gauge symmetry at all loop orders and highlights its importance in supersymmetry and scalar field theories.

Findings

MRI breakdown leads to quantum symmetry breakings.

MRI ensures gauge invariance at all loop levels.

MRI is essential for accurate renormalization group calculations.

Abstract

We illustrate with examples that quantum symmetry breakings in perturbation theory are connected to breakdown of momentum routing invariance (MRI) in the loops of a Feynman diagram. We show that MRI is a necessary and sufficient condition to preserve abelian gauge symmetry at arbitrary loop order. We adopt the implicit regularization framework in which surface terms that are directly connected to momentum routing can be constructed to arbitrary loop order. The interplay between momentum routing invariance, surface terms and anomalies is discussed. We also illustrate that MRI is important to preserve supersymmetry. For theories with poor symmetry content, such as scalar field theories, MRI is shown to be important in the calculation of renormalization group functions.