On knots in subdivergent diagrams

TL;DR

This paper explores the structure of certain Feynman diagrams, focusing on how their counterterms' transcendental properties relate to link diagram entanglement, revealing unexpected mathematical relations.

Contribution

It introduces a novel connection between the transcendental nature of counterterms and the entanglement in link diagrams derived from subdivergent Feynman diagrams.

Findings

Counterterms' transcendental properties reflect link diagram entanglement.

Unexpected relations between Feynman diagrams and link diagrams are identified.

Generalized one-loop functions facilitate the analysis of subdivergent diagrams.

Abstract

We investigate Feynman diagrams which are calculable in terms of generalized one-loop functions, and explore how the presence or absence of transcendentals in their counterterms reflects the entanglement of link diagram constructed from them and explains unexpected relations between them.