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.

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Correspondence to Fabien Vignes-Tourneret.

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Work supported by ANR grant NT05-3-43374 “GenoPhy”.

Submitted: June 30, 2006. Accepted: July 31, 2006.

Communicated by Raimar Wulkenhaar.

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Vignes-Tourneret, F. Renormalization of the Orientable Non-commutative Gross–Neveu Model. Ann. Henri Poincaré 8, 427–474 (2007). https://doi.org/10.1007/s00023-006-0312-6

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Keywords

  • External Variable
  • Power Counting
  • Gamma Matrice
  • Orientable Graph
  • Ribbon Graph