Renormalization of gauge theories without cohomology

TL;DR

This paper develops a renormalization method for gauge theories that does not rely on cohomological assumptions, ensuring the preservation of the master equation and accommodating non-linear solutions.

Contribution

It introduces a novel renormalization algorithm applicable to all anomaly-free gauge theories, generalizing to master functionals and field-covariant formalisms without cohomology.

Findings

Preserves the Batalin-Vilkovisky master equation at each renormalization step.

Automatically extends the classical action to absorb divergences.

Applicable to both power-counting renormalizable and non-renormalizable theories.

Abstract

We investigate the renormalization of gauge theories without assuming cohomological properties. We define a renormalization algorithm that preserves the Batalin-Vilkovisky master equation at each step and automatically extends the classical action till it contains sufficiently many independent parameters to reabsorb all divergences into parameter-redefinitions and canonical transformations. The construction is then generalized to the master functional and the field-covariant proper formalism for gauge theories. Our results hold in all manifestly anomaly-free gauge theories, power-counting renormalizable or not. The extension algorithm allows us to solve a quadratic problem, such as finding a sufficiently general solution of the master equation, even when it is not possible to reduce it to a linear (cohomological) problem.