Two-loop Feynman Diagrams in Yang-Mills Theory from Bosonic String Amplitudes

TL;DR

This paper explores extending one-loop Bern-Kosower rules to higher loops in Yang-Mills theory using bosonic string amplitudes, aiming to connect string diagrams with field theory results and address conceptual questions.

Contribution

It develops a general procedure to derive Yang-Mills Feynman diagrams from bosonic string amplitudes at higher loops, including technical tools and initial tests.

Findings

Reproduced known scalar and Yang-Mills results at one- and two-loop levels

Extracted universal renormalization coefficients for two-loop Yang-Mills diagrams

Identified conceptual questions about gauge choices and diagram relations that remain unresolved

Abstract

We present intermediate results of an ongoing investigation which attempts a generalization of the well known one-loop Bern Kosower rules of Yang-Mills theory to higher loop orders. We set up a general procedure to extract the field theoretical limit of bosonic open string diagrams, based on the sewing construction of higher loop world sheets. It is tested with one- and two-loop scalar field theory, as well as one-loop and two-loop vacuum Yang-Mills diagrams, reproducing earlier results. It is then applied to two-loop two-point Yang-Mills diagrams in order to extract universal renormalization coefficients that can be compared to field theory. While developing numerous technical tools to compute the relevant contributions, we hit upon important conceptual questions: Do string diagrams reproduce Yang-Mills Feynman diagrams in a certain preferred gauge? Do they employ a certain preferred renormalization scheme? Are four gluon vertices related to three gluon vertices? Unfortunately, our investigations remained inconclusive up to now.