Are Nonrenormalizable Gauge Theories Renormalizable?

TL;DR

This paper investigates whether gauge theories traditionally considered nonrenormalizable can be renormalized in the modern sense by using BRST cohomology, showing that certain nonrenormalizable theories are indeed renormalizable.

Contribution

It demonstrates that nonrenormalizable gauge theories can be renormalizable in the modern sense through BRST cohomology constraints, extending the class of renormalizable theories.

Findings

Nonrenormalizable theories can be renormalizable via BRST cohomology.

Yang-Mills theories with heavy quarks are renormalizable in this sense.

Gravitational theories are also shown to be renormalizable in the modern framework.

Abstract

We raise the issue whether gauge theories, that are not renormalizable in the usual power-counting sense, are nevertheless renormalizable in the modern sense that all divergences can be cancelled by renormalization of the infinite number of terms in the bare action. We find that a theory is renormalizable in this sense if the {\em a priori} constraints that we impose on the form of the bare action correspond to the cohomology of the BRST transformations generated by the action. Recent cohomology theorems of Barnich, Brandt, and Henneaux are used to show that conventionally nonrenormalizable theories of Yang-Mills fields (such as quantum chromodynamics with heavy quarks integrated out) and/or gravitation are renormalizable in the modern sense.