Bringing Yang-Mills theory closer to quasiclassics

A deformation of pure Yang-Mills theory by a phantom field similar to the Faddeev-Popov ghost is considered. In this theory an ersatz supersymmetry is identified which results in cancellation of quantum corrections up to two-loop order. A quadruplet built from two complex fields in the adjoint-the FaddeevPopov ghost c(a) and the phantom Phi(a), all with the wrong statistics-balances four gauge fields a(mu)(a). At this level, the instanton measure and the beta function are fully determined by quasiclassics. In a simple phi(4) theory with a phantom added I identify a strictly conserved ersatz supercurrent. In the latter theory unitarity of amplitudes persists despite the presence of the phantom. In deformed Yang-Mills it is likely (although not proven) to persist too in all amplitudes with only gluon external legs. It remains to be seen whether this construction is just a device facilitating some loop calculations or if broader applications can be found.

Automated summary

This study focuses on a deformation of pure Yang-Mills theory by a phantom field similar to the Faddeev-Popov ghost, revealing an ersatz supersymmetry that cancels quantum corrections up to two-loop order. By utilizing two complex fields with incorrect statistics, a quadruplet is constructed to balance gauge fields. Furthermore, it is suggested that unitarity of amplitudes persists even in the presence of the phantom, indicating potential broader applications beyond loop calculations.