CFT Zoo

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Next revision 		Previous revision
gross_neveu_model [2021/04/17 14:23]
Scott Lawrence created 		gross_neveu_model [2021/08/11 17:33] (current)
Scott Lawrence
Line 3: Line 3:
 {{tag>3d}} {{tag>3d}}
  
-[[https://arxiv.org/pdf/1011.1456.pdf]]+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 ===== ===== 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 one free fermion field).+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. In four dimensions this model is trivial.
 +
 +===== See also =====
 +
 +[[gross_neveu_yukawa_model]]
  
 ===== External links ===== ===== External links =====
  
-  * [[https://en.wikipedia.org/wiki/Gross%E2%80%93Neveu_model|Wikipedia]]+  * [[https://en.wikipedia.org/wiki/Gross%E2%80%93Neveu_model|Wikipedia]] only talks about the 2d model.
Last modified: 2021/04/17 14:23
CC Attribution-Noncommercial-Share Alike 4.0 International Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Noncommercial-Share Alike 4.0 International