Anomaly and Nonplanar Diagrams in Noncommutative Gauge Theories

Abstract

Anomalies arising from nonplanar triangle diagrams of noncommutative gauge theory are studied. Local chiral gauge anomalies for both noncommutative U(1) and U(N) gauge theories with adjoint matter fields are shown to vanish. For noncommutative QED with fundamental matters, due to UV/IR mixing a finite anomaly emerges from the nonplanar contributions. It involves a generalized $\star$-product of gauge fields.

28 pages, Latex, axodraw.sty; v2: version to appear in Int. J. Mod. Phys. A. (2001)

References in corpus (11)

• The IR/UV Connection in the Non-Commutative Gauge Theories
• Perturbative analysis on infrared aspects of noncommutative QED on R^4
• Strings in Background Electric Field, Space/Time Noncommutativity and A New Noncritical String Theory
• A Note on Background Independence in Noncommutative Gauge Theories, Matrix Model and Tachyon Condensation
• Complexified Gravity in Noncommutative Spaces
• The Origin of Chiral Anomaly and the Noncommutative Geometry
• Axial Anomaly in Noncommutative QED on R^4
• *-TREK: The One-Loop N=4 Noncommutative SYM Action
• Non-commutative world-volume interactions on D-brane and Dirac-Born-Infeld action
• Noncommutative perturbation in superspace
• A Note on Gauge Invariant Operators in Noncommutative Gauge Theories and the Matrix Model

Cited by in corpus (27)

• Ginsparg-Wilson Relation, Topological Invariants and Finite Noncommutative Geometry
• Ginsparg-Wilson Relation and 't Hooft-Polyakov Monopole on Fuzzy 2-Sphere
• Chiral Anomaly on Fuzzy 2-Sphere
• Nonplanar Anomalies in Noncommutative Theories and the Green-Schwarz Mechanism
• Trouble with space-like noncommutative field theory
• Telltale Traces of U(1) Fields in Noncommutative Standard Model Extensions
• Heat kernel, effective action and anomalies in noncommutative theories
• The Z--> l^+ l^- and W--> nu_l l^+ decays in the noncommutative standard model}}
• Lattice Perturbation Theory in Noncommutative Geometry and Parity Anomaly in 3D Noncommutative QED
• BRST Quantization of Noncommutative Gauge Theories
• Bosonized noncommutative bi-fundamental fermion and S-duality
• On the mass spectrum of noncommutative Schwinger model in Euclidean ${\mathbb{R}}^2$ space
• Axial anomaly of QED in a strong magnetic field and noncommutative anomaly
• The inclusive b -> s γdecay in the noncommutative standard model
• Seiberg-Witten maps and commutator anomalies in noncommutative electrodynamics
• Translational-invariant noncommutative gauge theory
• UV/IR Mixing and Anomalies in Noncommutative Gauge Theories
• Noncommutative Dipole QED
• A Noncommutative Version of the Minimal Supersymmetric Standard Model
• Dynamics of O(N) Model in a Strong Magnetic Background Field as a Modified Noncommutative Field Theory
• Consistent Anomalies in Translation-Invariant Noncommutative Gauge Theories
• On the Anomalies and Schwinger Terms in Noncommutative Gauge Theories
• Open-String Actions and Noncommutativity Beyond the Large-B Limit
• Conformal Anomalies in Noncommutative Gauge Theories
• Planar and Nonplanar Konishi Anomalies and Effective Superpotential for Noncommutative N=1 Supersymmetric U(1)
• The form factors existing in the b->s g^* decay and the possible CP violating effects in the noncommutative standard model
• Search for noncommutative interactions in $\gamma \gamma \to \gamma \gamma$ process at the LHC