Noncommutative Linear Sigma Models

Abstract

We examine noncommutative linear sigma models with U(N) global symmetry groups at the one-loop quantum level, and contrast the results with our previous study of the noncommutative O(N) linear sigma models where we have shown that Nambu-Goldstone symmetry realization is inconsistent with continuum renormalization. Specifically we find no violation of Goldstone's theorem at one-loop for the U(N) models with the quartic term ordering consistent with possible noncommutative gauging of the model. The difference is due to terms involving noncommutative commutator interactions, which vanish in the commutative limit. We also examine the U(2), and O(4) linear sigma models with matter in the adjoint representation, and find that the former is consistent with Goldstone's theorem at one-loop if we include only trace invariants consistent with possible noncommutative gauging of the model, while the latter exhibits violations of Goldstone's theorem of the kind seen in the fundamental of O(N) for N>2.

23 pages, Latex, uses feynmp

Cited by in corpus (15)

• Noncommutative Field Theory
• Quantum Field Theory on Noncommutative Spaces
• Vacuum configurations for renormalizable non-commutative scalar models
• Non-Commutativity and Unitarity Violation in Gauge Boson Scattering
• Noncommutative geometry, gauge theory and renormalization
• UV/IR mixing and the Goldstone theorem in noncommutative field theory
• On the UV renormalizability of noncommutative field theories
• Spontaneous Symmetry Breaking in Noncommutative Field Theory
• Validity of Goldstone Theorem at Two Loops in Noncommutative U(N) Linear Sigma Model
• The three-dimensional noncommutative Gross-Neveu model
• One Loop Renormalizability of Spontaneously Broken Gauge Theory with a Product of Gauge Groups on Noncommutative Spacetime: the U(1) x U(1) Case
• Color Grosse-Wulkenhaar models: One-loop $\beta$-functions
• Wave Propagation and IR/UV Mixing in Noncommutative Spacetimes
• Supersymmetry and Gravity in Noncommutative Field Theories
• The Slavnov-Taylor Identities for the 2+1 Dimensional Noncommutative CP${}^{N-1}$ Model