Is Yang-Mills Theory Unitary in Fractional Spacetime Dimensions?

TL;DR

This paper provides evidence that Yang-Mills theory becomes non-unitary in fractional spacetime dimensions due to evanescent operators causing negative-norm states and complex anomalous dimensions.

Contribution

It demonstrates that evanescent operators induce non-unitarity in Yang-Mills theory in non-integer dimensions, a novel insight into its dimensional behavior.

Findings

Evanescent operators are non-zero in non-integer dimensions.

Negative-norm states emerge in fractional dimensions.

Complex anomalous dimensions appear in the theory.

Abstract

We present concrete evidence that Yang-Mills theory exhibits non-unitarity in non-integer spacetime dimensions. This violation of unitarity stems from evanescent operators that, while vanishing in four dimensions, are non-zero in general d dimensions. We demonstrate that these evanescent operators lead to the emergence of both negative-norm states and complex anomalous dimensions.