Vortex stability in pseudo-Hermitian theories

TL;DR

This paper demonstrates that vortex solutions in pseudo-Hermitian field theories can exhibit metastability due to small symmetry breaking, leading to complex spectra and potential cosmological implications.

Contribution

It provides the first analytical and numerical analysis of vortex metastability in pseudo-Hermitian theories caused by symmetry breaking effects.

Findings

Vortex solutions show metastability despite parameters suggesting stability.

Small symmetry breaking induces complex frequencies and exceptional points.

Metastable vortices have potential applications in cosmology.

Abstract

Pseudo-Hermitian (including $\mathcal{PT}$-symmetric) field theories support phenomenology that cannot be replicated in standard Hermitian theories. We describe a concrete example in which the vortex solutions that are realised in a prototypical pseudo-Hermitian field theory exhibit a novel metastability, despite the model parameters residing within the naively stable regime of exact antilinear symmetry of the vacuum theory. This instability is identified analytically and confirmed through numerical simulations, and it arises from the small breaking of the underlying antilinear symmetry of the pseudo-Hermitian theory due to the presence of the topological defect. This leads to spacetime-dependent parameters in the equations of motion governing fluctuations around the vortex, inducing non-trivial exceptional-point structures and complex frequencies within their spectrum. Aside from offering intriguing possibilities for cosmology, this result serves to illustrate the ability to produce long-lived metastable configurations in pseudo-Hermitian field theories of relevance beyond cosmology and high energy physics.