Supersymmetric field theory with benign ghosts

TL;DR

This paper develops a (1+1)-dimensional supersymmetric field theory with ghosts that, despite having an unbounded Hamiltonian spectrum, remains stable and unitary at both classical and quantum levels.

Contribution

It introduces a novel supersymmetric field theory with higher derivatives and ghosts that does not suffer from collapse or loss of unitarity.

Findings

Spectrum of the Hamiltonian is unbounded from below and above.

The theory remains stable and unitary despite the unbounded spectrum.

Abstract

We construct a supersymmetric (1+1)-dimensional field theory involving extra derivatives and associated ghosts: the spectrum of the Hamiltonian is not bounded from below, neither from above. In spite of that, there is neither classical, nor quantum collapse and unitarity is preserved.