The Noncommutative Supersymmetric Nonlinear Sigma Model

Details The Noncommutative Supersymmetric Nonlinear Sigma Model The Noncommutative Supersymmetric Nonlinear Sigma Model

2001-02-16

arxiv.org/abs/hep-th/0102101v2

Int.J.Mod.Phys. A17 (2002) 1503-1516

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, 7 figures, revtex, minor modifications in the text, references added

Scientific paper

10.1142/S0217751X02009850

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.

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