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Non-commutative Gross-Neveu model at large N

Emil T. Akhmedov·Philip DeBoer·Gordon W. Semenoff
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Abstract

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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Emil T. Akhmedov, Philip DeBoer, Gordon W. Semenoff. 2001-04-05. Non-commutative Gross-Neveu model at large N. https://doi.org/10.1088/1126-6708%2F2001%2F06%2F009

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