Quantum field theory with ghost pairs

TL;DR

This paper proves that certain higher-derivative quantum field theories with complex conjugate ghosts are unitary at all perturbative orders by complex energy integration techniques, with implications for quantum gravity and gauge theories.

Contribution

It introduces a novel complex energy integration method to establish unitarity in higher-derivative theories with ghost pairs, extending previous nonlocal theory approaches.

Findings

Higher-derivative theories with ghost pairs are unitary at all orders.

Complex ghosts can be present without appearing as asymptotic states.

Application to gravitational and gauge theories shows unitarity when ghosts are excluded from the spectrum.

Abstract

We explicitly show that general local higher-derivative theories with only complex conjugate ghosts and normal real particles are unitary at any perturbative order in the loop expansion. The proof presented here relies on integrating the loop energies on complex paths resulting from the deformation of the purely imaginary paths, when the external energies are continued from imaginary to real values. Contrary to the case of nonlocal theories, where the same integration path was first proposed, for the classes of theories studied here the same procedure is not analytic, but the resulting theory is unitary and unique when the complex ghosts are present in pairs. As an explicit application, a special class of higher-derivative super-renormalizable or finite gravitational and gauge theories turns out to be unitary at any perturbative order if we exclude the complex ghosts from the spectrum of the theory, as it is normally accepted for Becchi-Rouet-Stora-Tyutin (BRST) ghosts. Finally, we propose an analogy between confined gluons in quantum Yang-Mills theory and classical complex pairs in local higher-derivative theories. According to such interpretation, complex ghosts will not appear on shell as asymptotic states because confined in what is natural to name "ghostballs."