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

Abstract

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].

9 pages, 4 figures; Reference added

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Cited by in corpus (4)

• Unitarity and Universality in non relativistic Conformal Field theory
• On operator mixing in fermionic CFTs in non-integer dimensions
• Disturbing news about the $d=2+\epsilon$ expansion
• Analytic Studies of Fermions in the Conformal Bootstrap