Bringing Yang-Mills Theory Closer to Quasiclassics

TL;DR

This paper introduces a deformed Yang-Mills theory with a phantom field that exhibits supersymmetry-like cancellations of quantum corrections, potentially simplifying loop calculations while maintaining unitarity.

Contribution

It identifies an Ersatz-supersymmetry in a phantom-deformed Yang-Mills theory that cancels quantum corrections up to two loops and preserves unitarity despite the phantom fields.

Findings

Quantum corrections canceled up to two loops.

Unitarity persists despite phantom fields.

Potential simplification of loop calculations in Yang-Mills.

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.