Benign vs malicious ghosts in higher-derivative theories

TL;DR

This paper explores the stability of higher-derivative theories, distinguishing between benign and malicious ghosts, and presents examples of benign theories that are stable under small perturbations but exhibit nonperturbative instabilities.

Contribution

It introduces the concept of benign higher-derivative theories that are stable at the classical and perturbative levels, exemplified by a 6D N=2 higher-derivative SYM theory.

Findings

Benign higher-derivative systems can be classically stable.

Perturbative stability does not imply nonperturbative stability.

The 6D N=2 higher-derivative SYM theory is finite and unitary at the perturbative level.

Abstract

Interacting theories with higher derivatives involve ghosts. They correspond to instabilities that display themselves at the classical level. We notice that comparatively "benign" mechanical higher-derivative systems exist where the classical vacuum is stable with respect to small perturbations and the problems appear only at the nonperturbative level. We argue that benign higher-derivative field theories exist which are stable with respect to small fluctuations with nonzero momenta. A particular example is the 6D N=2 higher-derivative SYM theory, which is finite and unitary at the perturbative level. The inflation-like instability with respect to small fluctuations of static modes is always present, however.