Non-commutative Gross-Neveu model at large N

Details Non-commutative Gross-Neveu model at large N Non-commutative Gross-Neveu model at large N

2001-03-23

arxiv.org/abs/hep-th/0103199v2

JHEP 0106 (2001) 009

Physics

High Energy Physics

High Energy Physics - Theory

23 pages

Scientific paper

10.1088/1126-6708/2001/06/009

The non-commutative O(N) Gross-Neveu model is solved in the large N limit in two and three space-time dimensions. The commutative version of the two dimensional model is a renormalizable quantum field theory, both in a coupling constant expansion and an expansion in 1/N. The non-commutative version has a renormalizable coupling constant expansion where ultraviolet divergences can be removed by adjusting counterterms to each order. On the other hand, in a previous work, we showed that the non-commutative theory is not renormalizable in the large N expansion. This is argued to be due to a combined effect of asymptotic freedom and the ultraviolet/infrared mixing that occurs in a non-commutative field theory. In the present paper we will elaborate on this result and extend it to study the large N limit of the three dimensional Gross-Neveu model. We shall see that the large N limit of the three dimensional theory is also trivial when the ultraviolet cutoff is removed.

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