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.

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

References in corpus (4)

• The Three-Dimensional Noncommutative Nonlinear Sigma Model in Superspace
• The Higgs Mechanism in Non-commutative Gauge Theories
• Hard Non-commutative Loops Resummation
• Non-commutative Gross-Neveu model at large N

Cited by in corpus (28)

• Noncommutative Field Theory
• Quantum Field Theory on Noncommutative Spaces
• Noncommutative Field Theories and Gravity
• Exact Solution of Quantum Field Theory on Noncommutative Phase Spaces
• On the Horava-Lifshitz-like Gross-Neveu model
• D=2, N=2, Supersymmetric theories on Non(anti)commutative Superspace
• Dispersion Relations in Noncommutative Theories
• On the UV renormalizability of noncommutative field theories
• Supersymmetric Quantum Mechanics on Non-Commutative Plane
• Superfield Effective Action in the Noncommutative Wess-Zumino Model
• Spontaneous Symmetry Breaking in Noncommutative Field Theory
• Noncommutative Maxwell-Chern-Simons theory in three dimensions and its dual
• The low energy limit of the non-commutative Wess-Zumino model
• N=2 sigma model Action on Non(anti)commutative Superspace
• On the finiteness of the noncommutative supersymmetric Maxwell-Chern-Simons theory
• The coupling of fermions to the three-dimensional noncommutative $C{P}^{N-1}$ model: minimal and supersymmetric extensions
• O(3) Sigma model with Hopf term on Fuzzy Sphere
• The three-dimensional noncommutative Gross-Neveu model
• Noncommutative Supersymmetry in Two Dimensions
• Non-commutative Duality: High Spin Fields and $C{P}^1$ Model with Hopf Term
• (2+1)D Noncommutative CP${}^{N-1}$ Model
• Supersymmetry breaking in the three-dimensional nonlinear sigma model
• Supersymmetric Extension of the Snyder Algebra
• Supersymmetry and Gravity in Noncommutative Field Theories
• Soft supersymmetry breaking in the nonlinear sigma model
• The 1/N Expansion in Noncommutative Quantum Mechanics
• Noncommutative Supersymmetric Field Theories
• Noncommutative Theories, Seiberg-Witten Map and Gravity