Geodesic
Proof of the absence of multiplicative renormalizability of the Gross–Neveu model in dimensional regularization $d=2+2\varepsilon$
Teoretičeskaâ i matematičeskaâ fizika, Tome 113 (1997) no. 1, pp. 85-99 Cet article a éte moissonné depuis la source Math-Net.Ru

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We prove that the simplest four-fermion Gross–Neveu model with dimensional regularization $d=2+2\varepsilon$ is not multiplicatively renormalizable due to the counterterm generated by the three-loop vertex diagrams that is proportional to the evanescent operator [1] $V_3=(\bar\psi\gamma_{ikl}^{(3)}\psi )^2/2$, where $\gamma_{i_1\dots i_n}^{(n)}$ is the fully antisymmetric product of $n$ $\gamma$-matrices and is not zero in arbitrary dimensions. Therefore, calculations of the $(2+\varepsilon)$-expansion of the critical indices $\eta$ and $\nu$ in the framework of the simple Gross–Neveu model are correct only to $\varepsilon^4$ for $\eta$ and to $\varepsilon^3$ for $\nu$. In higher orders, one must take into consideration the generation of other (not only $V_3$) evanescent operators. 
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     title = {Proof of the absence of multiplicative renormalizability of the {Gross{\textendash}Neveu} model in dimensional regularization $d=2+2\varepsilon$},
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A. N. Vasil'ev; M. I. Vyazovskii. Proof of the absence of multiplicative renormalizability of the Gross–Neveu model in dimensional regularization $d=2+2\varepsilon$. Teoretičeskaâ i matematičeskaâ fizika, Tome 113 (1997) no. 1, pp. 85-99. http://geodesic.mathdoc.fr/item/TMF_1997_113_1_a7/

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