String techniques for the calculation of renormalization constants in field theory

TL;DR

This paper develops string theory-based methods to calculate gauge theory renormalization constants, demonstrating their consistency and relation to Feynman diagrams, and deriving a multiloop effective action expression.

Contribution

It introduces a novel prescription for off-shell open bosonic string amplitudes to compute renormalization constants in gauge theories, linking string moduli space regions to Feynman diagram classes.

Findings

Validated the prescription through explicit amplitude calculations.

Identified string moduli regions corresponding to Feynman diagrams.

Derived a multiloop effective action expression.

Abstract

We describe a set of methods to calculate gauge theory renormalization constants from string theory, all based on a consistent prescription to continue off shell open bosonic string amplitudes. We prove the consistency of our prescription by explicitly evaluating the renormalizations of the two, three and four-gluon amplitudes, and showing that they obey the appropriate Ward identities. The field theory limit thus performed corresponds to the background field method in Feynman gauge. We identify precisely the regions in string moduli space that correspond to different classes of Feynman diagrams, and in particular we show how to isolate contributions to the effective action. Ultraviolet divergent terms are then encoded in a single string integral over the modular parameter $\tau$. Finally, we derive a multiloop expression for the effective action by computing the partition function of an open bosonic string interacting with an external non-abelian background gauge field.