Bringing Yang-Mills Theory Closer to Quasiclassics

Abstract

A deformation of pure Yang-Mill theory by a phantom field similar to the Faddeev-Popov ghost is considered. In this theory an {\em 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 Faddeev-Popov 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 is fully determined by quasiclassics. In a simple $\phi^4$ theory with a phantom added I identify a strictly conserved {\em 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 broader applications can be found.