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The Noncommutative Supersymmetric Nonlinear Sigma Model

H. O. Girotti·M. Gomes·V. O. Rivelles·A. J. da Silva
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Abstract

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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H. O. Girotti, M. Gomes, V. O. Rivelles, A. J. da Silva. 2001-06-13. The Noncommutative Supersymmetric Nonlinear Sigma Model. https://doi.org/10.1142/s0217751x02009850

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