Complex BPS Skyrmions with real energy

TL;DR

This paper explores complex extensions of the Skyrme model, revealing new BPS solutions with real energies, including step, cusp, shell, and purely imaginary compactons, through a modified CPT-symmetry framework.

Contribution

It introduces novel complex BPS Skyrmion solutions and a symmetry-based method to ensure their real energies, expanding the understanding of Skyrme model configurations.

Findings

Discovery of new BPS solutions: step, cusp, shell, and purely imaginary compactons.

Demonstration of real energies via a modified CPT-symmetry mapping.

Extension of the Skyrme model with complex solutions maintaining physical relevance.

Abstract

We propose and investigate several complex versions of extensions and restrictions of the Skyrme model with a well-defined Bogomolny-Prasad-Sommerfield (BPS) limit. The models studied possess complex kink, anti-kink, semi-kink, massless and purely imaginary compacton BPS solutions that all have real energies. The reality of the energies for a particular solution is guaranteed when a modified antilinear CPT-symmetry maps the Hamiltonian functional to its parity time-reversed complex conjugate and the solution field to itself or a new field with degenerate energy. In addition to the known BPS Skyrmion configurations we find new types that we refer to as step, cusp, shell, and purely imaginary compacton solutions.