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

TL;DR

This paper demonstrates unitarity violation in a non-integer dimensional fermionic quantum field theory by analyzing the anomalous dimensions of four-fermion operators in the Gross-Neveu-Yukawa model, revealing negative norm states.

Contribution

It provides an explicit example of unitarity violation in non-integer dimensions through one-loop analysis of four-fermion operators in the Gross-Neveu-Yukawa model.

Findings

Four-fermion operators split into three classes at one loop

One class of operators has negative norms

The theory violates unitarity as per the defined criteria

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].