Supersymmetry without hermiticity

TL;DR

This paper introduces a novel supersymmetry model where states have PT symmetry and real energies, but the partner Hamiltonians are complex and non-Hermitian, challenging traditional assumptions.

Contribution

It proposes a new supersymmetry framework with PT-symmetric states and non-Hermitian Hamiltonians, expanding the theoretical landscape.

Findings

States exhibit PT symmetry with real energies

Partner Hamiltonians are complex and non-Hermitian

Witten index can vanish in this formalism

Abstract

A new model of supersymmetry between bosons and fermions is proposed. Its representation space is spanned by states with PT symmetry and real energies but the inter-related partner Hamiltonians themselves remain complex and non-Hermitian. The formalism admits vanishing Witten index.