Physics of crypto-Hermitian and/or cryptosupersymmetric field theories

TL;DR

This paper explores non-Hermitian quantum field theories with real spectra, focusing on supersymmetric deformations and their spectral properties, including supersymmetry preservation and issues with S-matrix unitarity.

Contribution

It demonstrates that certain non-Hermitian, supersymmetry-deformed field theories have real spectra and retain supersymmetry algebra, despite potential non-unitarity of the S-matrix.

Findings

Deformed theories often have real energy spectra.

Half of the supersymmetries are manifest in these theories.

The S-matrix in such theories is generally not unitary.

Abstract

We discuss non-Hermitian field theories where the spectrum of the Hamiltonian involves only real energies. We make three observations. (i) The theories obtained from supersymmetric theories by nonanticommutative deformations belong in many cases to this class. (ii) When the deformation parameter is small, the deformed theory enjoys the same supersymmetry algebra as the undeformed one. Half of the supersymmetries are manifest and the existence of another half can be deduced from the structure of the spectrum. (iii) Generically, the conventionally defined S--matrix is not unitary for such theories.