Quantum field theory with ghost pairs

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.

Automated summary

In this paper, we demonstrate 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. By integrating the loop energies on complex paths resulting from the deformation of the purely imaginary paths, the proof of unitarity is established. The exclusion of complex ghosts from the spectrum of the theory, as commonly done for Becchi-Rouet-Stora-Tyutin (BRST) ghosts, leads to the unitarity of a specific class of higher-derivative super-renormalizable or finite gravitational and gauge theories at any perturbative order.