The Gross-Neveu model is a theory of $N$ interacting fermions defined by the Lagrangian density \[\require{cancel} L = \bar\psi i \cancel{\partial} \psi + \frac{g^2}{2N} (\bar\psi \psi)^2 \text. \]

This model is usually studied in two dimensions, where it is asymptotically free for any $N$. However, for $2 < d < 4$, the theory is asymptotically safe: https://arxiv.org/pdf/1011.1456.pdf. Thus, there's a nontrivial CFT corresponding to the UV fixed point. This page is about that CFT.

It is more common to study the Gross-Neveu model in two dimensions, where it is asymptotically free (so that the fixed point coincides with the theory of one free fermion field).

In four dimensions this model is trivial.

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