Gauge invariance and the Englert-Brout-Higgs mechanism in non-Hermitian field theories

TL;DR

This paper explores gauge invariance and the Englert-Brout-Higgs mechanism within non-Hermitian, PT-symmetric field theories, proposing a consistent framework that could extend the Standard Model.

Contribution

It generalizes the Englert-Brout-Higgs mechanism to PT-symmetric non-Hermitian field theories, addressing gauge invariance issues and proposing a novel coupling to non-conserved currents.

Findings

Gauge invariance challenges are addressed in non-Hermitian theories.

A consistent formulation of the Higgs mechanism in PT-symmetric models is proposed.

Potential for extending the Standard Model with non-Hermitian field theories.

Abstract

We discuss $\mathcal{PT}$-symmetric Abelian gauge field theories, as well as their extension to the Englert-Brout-Higgs mechanism for generating a mass for a vector boson. Gauge invariance is not straightforward, and we discuss the different related problems, as well as a solution which consists in coupling the gauge field to a current that is not conserved. Non-Hermiticity then necessarily precludes the Lorenz gauge condition but nevertheless allows for a consistent formulation of the theory. We therefore generalise the Englert-Brout-Higgs mechanism to $\mathcal{PT}$-symmetric field theories, opening the way to constructing non-Hermitian extensions of the Standard Model and new scenarios for particle model-building.