Non-Hermitian gauge field theories and BPS limits

TL;DR

This paper explores non-Hermitian gauge field theories, focusing on symmetry modifications, BPS limits, and their implications for mass spectra, monopoles, and soliton solutions across various dimensions.

Contribution

It provides a systematic analysis of non-Hermitian gauge theories, extending Goldstone's theorem and Higgs mechanism, and identifies new complex solutions with real energies.

Findings

Reality of mass spectrum guaranteed by CPT-symmetries

Identification of t'Hooft-Polyakov monopoles via BPS limit in non-Hermitian theories

Discovery of new complex soliton solutions with real energies

Abstract

We present an overview of some key results obtained in a recent series devoted to non-Hermitian quantum field theories for which we systematically modify the underlying symmetries. Particular attention is placed on the interplay between the continuous symmetry group that we alter from global to local, from Abelian to non-Abelian, from rank one to generic rank N, and the discrete anti-linear modified CPT-symmetries. The presence of the latter guarantees the reality of the mass spectrum in a certain parameter regime. We investigate the extension of Goldstone's theorem and the Higgs mechanism, which we demonstrate to work in the conventional fashion in the CPT symmetric regime, but which needs to be modified technically at the standard exceptional points of the mass spectrum and entirely fails at what we refer to as zero exceptional points as well as in the broken CPT-symmetric regime. In the full non-Hermitian non-Abelian gauge theory we identify the t'Hooft-Polyakov monopoles by means of a fourfold Bogomol'nyi-Prasad-Sommerfield (BPS) limit. We investigate this limit further for other types of non-Hermitian field theories in 1+1 dimensions that possess complex super-exponential and inverse hyperbolic kink/anti-kink solutions and for 3+1 dimensional Skyrme models for which we find new types of complex solutions, that all have real energies due to the presence of different types of CPT-symmetries.