2001/02/28 by H. O. Girotti, M. Gomes, Victor O. Rivelles +2 · 3 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #Particle physics theoretical and experimental studies #hep-th
paper · pdf · doi:10.1142/s0217751x02009850
published as Int.J.Mod.Phys. A17 (2002) 1503-1516 · 15 pages, 7 figures, revtex, minor modifications in the text, references added
arxiv created 2001/06/13 · openalex publication_date 2002/04/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the noncommutativity of space–time destroys the renormalizability of the 1/N expansion of the O(N) Gross–Neveu model. A similar statement holds for the noncommutative nonlinear sigma model. However, we show that, up to the subleading order in 1/N expansion, the noncommutative supersymmetric O(N) nonlinear sigma model becomes renormalizable in D=3. We also show that dynamical mass generation is restored and there is no catastrophic UV/IR mixing. Unlike the commutative case, we find that the Lagrange multiplier fields, which enforce the supersymmetric constraints, are also renormalized. For D=2 the divergence of the four-point function of the basic scalar field, which in D=3 is absent, cannot be eliminated by means of a counterterm having the structure of a Moyal product.