Emil T. Akhmedov et al JHEP06(2001)009 doi:10.1088/1126-6708/2001/06/009
Non-commutative Gross-Neveu model at large N
Emil T. Akhmedov1, Philip DeBoer1 and Gordon W. Semenoff1
Show affiliationsThe 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 [1] 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.
- Keywords
- PACS
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11.10.Nx Noncommutative field theory
- Subjects
- Dates
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Issue 06 ( 1 June 2001)
Received 6 April 2001, accepted for publication 2 June 2001
Published 4 July 2001
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Non-commutative Gross-Neveu model at large N
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