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We construct an explicit example of unitarity violation in fermionic quantumfield theories in non-integer dimensions. We study the two-point correlationfunction of four-fermion operators. We compute the one-loop anomalousdimensions of these operators in the Gross-Neveu-Yukawa Model. We find that atone loop order, the four-fermion operators split into three classes with oneclass having negative norms. This implies that the theory violates unitarityfollowing the definition in arXiv:1512.00013 [hep-th].

Unitarity violation in non-integer dimensional Gross-Neveu-Yukawa model