Confinement of massive ghost in quadratic gravity

In the framework of the covariant canonical formalism of quadratic gravity, we consider the problem of confinement of massive ghost which violates the unitarity of the physical S-matrix. It is shown that if there is a bound state between the massive ghost and Faddeev–Popov ghost the massive ghost is confined in the zero-norm states through the BRST quartet mechanism, thereby the unitarity being restored. Based on the superfield formulation by Bonora and Tonin, we show that the asymptotic field of the massive ghost must be a massive dipole whereas that of the bound state obeys a massive Klein–Gordon equation. This situation may be of some similarity to color confinement in quantum chromodynamics (QCD) where it is conjectured that not a massless but a massive gluon is in fact confined.