We construct an explicit example of unitarity violation in fermionic quantum field theories in non-integer dimensions. We study the two-point correlation function of four-fermion operators. We compute the one-loop anomalous dimensions of these operators in the Gross-Neveu-Yukawa Model. We find that at one loop order, the four-fermion operators split into three classes with one class having negative norms. This implies that the theory violates unitarity following the definition in arXiv:1512.00013 [hep-th].
@article{arxiv.1802.03222,
title = {Unitarity violation in non-integer dimensional Gross-Neveu-Yukawa model},
author = {Yao Ji and Michael Kelly},
journal= {arXiv preprint arXiv:1802.03222},
year = {2018}
}