Complex BPS solitons with real energies from duality

TL;DR

This paper explores complex non-Hermitian field theories with BPS solitons, demonstrating that despite their complex nature, these solutions have real energies due to topological and symmetry properties, expanding understanding of non-Hermitian models.

Contribution

It introduces new complex BPS soliton solutions in non-Hermitian theories and shows their energies are real through a pseudo-Hermitian framework and topological arguments.

Findings

Complex BPS solitons possess real energies.

Energy equivalence between non-Hermitian and Hermitian models.

Topological properties ensure energy reality despite non-Hermiticity.

Abstract

Following a generic approach that leads to Bogomolny-Prasad-Sommerfield (BPS) soliton solutions by imposing self-duality, we investigate three different types of non-Hermitian field theories. We consider a complex version of a logarithmic potential that possess BPS super-exponential kink and antikink solutions and two different types of complex generalisations of systems of coupled sine-Gordon models with kink and antikink solution of complex versions of arctan type. Despite the fact that all soliton solutions obtainedin this manner are complex in the non-Hermitian theories we show that they possess real energies. For the complex extended sine-Gordon model we establish explicitly that the energies are the same as those in an equivalent pair of a non-Hermitian and Hermitian theory obtained from a pseudo-Hermitian approach by means of a Dyson map. We argue that the reality of the energy is due to the topological properties of the complex BPS solutions. These properties result in general from modified versions of antilinear CPT symmetries that relate self-dual and an anti-self-dual theories.