Renormalization in string-localized field theories: a microlocal analysis

TL;DR

This paper demonstrates that in string-localized field theories, the regularization of divergent amplitudes remains an ultraviolet issue, preserving the relevance of power counting for renormalizability despite weaker localization.

Contribution

It applies microlocal analysis to show that regularization in string-localized theories is an ultraviolet problem, maintaining the importance of power counting for renormalizability.

Findings

Regularization remains an ultraviolet problem in string-localized theories.

Power counting remains a valid indicator for renormalizability.

Standard regularization techniques are applicable in string-localized field theories.

Abstract

Using methods of microlocal analysis, we prove that the regularization of divergent amplitudes stays a pure ultraviolet problem in string-localized field theories, despite the weaker localization. Thus, power counting does not lose its significance as an indicator for renormalizability. It also follows that standard techniques can be used to regularize divergent amplitudes in string-localized field theories.