Renormalizability of the Dynamical Two-Form

TL;DR

This paper proves the renormalizability of a non-Abelian two-form gauge theory using novel symmetries, demonstrating a consistent quantum theory of massive vector bosons without a Higgs mechanism.

Contribution

It introduces two new symmetries necessary for proving renormalizability and extends the BRST symmetry to include shift transformations.

Findings

The theory is renormalizable to all orders in perturbation theory.

New symmetries constrain the quantum action's form.

Massive vector bosons can be described without a residual Higgs boson.

Abstract

A proof of renormalizability of the theory of the dynamical non-Abelian two-form is given using the Zinn-Justin equation. Two previously unknown symmetries of the quantum action, different from the BRST symmetry, are needed for the proof. One of these is a gauge fermion dependent nilpotent symmetry, while the other mixes different fields with the same transformation properties. The BRST symmetry itself is extended to include a shift transformation by use of an anticommuting constant. These three symmetries restrict the form of the quantum action up to arbitrary order in perturbation theory. The results show that it is possible to have a renormalizable theory of massive vector bosons in four dimensions without a residual Higgs boson.