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 Faddeev-Popov ghost ca and the phantom φa, all with the wrong statistics - balances four gauge fields aμa. At this level, the instanton measure and the β function are fully determined by quasiclassics. In a simple φ4 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.
Bibliographical noteFunding Information:
I am grateful to A. Cherman, G. Dunne, and M. Ünsal for useful communications. This work is supported in part by DOE Grant No. de-sc0011842.
© 2021 authors. Published by the American Physical Society.