Table of Contents

Gross-Neveu model

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

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.

Large-N Limit

https://www.sciencedirect.com/science/article/pii/037026939291265B?via%3Dihub

Other dimensions

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 $N$ free fermion fields).

In four dimensions this model is trivial.

See also

Gross-Neveu-Yukawa model