The Noncommutative Supersymmetric Nonlinear Sigma Model
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.
Cite
@article{arxiv.hep-th/0102101,
title = {The Noncommutative Supersymmetric Nonlinear Sigma Model},
author = {H. O. Girotti and M. Gomes and V. O. Rivelles and A. J. da Silva},
journal= {arXiv preprint arXiv:hep-th/0102101},
year = {2009}
}
Comments
15 pages, 7 figures, revtex, minor modifications in the text, references added