Benign vs. malicious ghosts in higher-derivative theories

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 the existence of benign higher-derivative field theories 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 instability with respect to small fluctuations of zero-momentum modes is always present, however.