, Volume 8, Issue 3, pp 427-474,
Open Access This content is freely available online to anyone, anywhere at any time.

Renormalization of the Orientable Non-commutative Gross–Neveu Model

Abstract.

We prove that the non-commutative Gross–Neveu model on the two-dimensional Moyal plane is renormalizable to all orders. Despite a remaining UV/IR mixing, renormalizability can be achieved. However, in the massive case, this forces us to introduce an additional counterterm of the form \(\bar{\psi}\imath\gamma^{0}\gamma^{1}\psi\) . The massless case is renormalizable without such an addition.

Communicated by Raimar Wulkenhaar.
Work supported by ANR grant NT05-3-43374 “GenoPhy”.
Submitted: June 30, 2006. Accepted: July 31, 2006.