*-Wars Episode I: The Phantom Anomaly

Abstract

As pointed out, chiral non-commutative theories exist, and examples can be constructed via string theory. Gauge anomalies require the matter content of individual gauge group factors, including U(1) factors, to be non-chiral. All ``bad'' mixed gauge anomalies, and also all ``good'' (e.g. for ${\pi }^0\to \gamma \gamma$) ABJ type flavor anomalies, automatically vanish in non-commutative gauge theories. We interpret this as being analogous to string theory, and an example of UV/IR mixing: non-commutative gauge theories automatically contain ``closed string,'' Green-Schwarz fields, which cancel these anomalies.

20 pages. Added references and minor typos corrected

References in corpus (1)

• Gauge-Invariant Couplings of Noncommutative Branes to Ramond-Ramond Backgrounds

Cited by in corpus (18)

• Noncommutative Standard Model: Model Building
• Nonplanar Anomalies in Noncommutative Theories and the Green-Schwarz Mechanism
• Telltale Traces of U(1) Fields in Noncommutative Standard Model Extensions
• Heat kernel, effective action and anomalies in noncommutative theories
• Noncommutative Standard Modelling
• Lattice Perturbation Theory in Noncommutative Geometry and Parity Anomaly in 3D Noncommutative QED
• Anomalies in noncommutative gauge theories, Seiberg-Witten transformation and Ramond-Ramond couplings
• Axial anomaly of QED in a strong magnetic field and noncommutative anomaly
• Noncommutativity and Model Building
• Translational-invariant noncommutative gauge theory
• UV/IR Mixing and Anomalies in Noncommutative Gauge Theories
• Effective actions, Wilson lines and the IR/UV mixing in noncommutative supersymmetric gauge theories
• The U(1)A anomaly in noncommutative SU(N) theories
• Consistent Anomalies in Translation-Invariant Noncommutative Gauge Theories
• On the Anomalies and Schwinger Terms in Noncommutative Gauge Theories
• Conformal Anomalies in Noncommutative Gauge Theories
• Planar and Nonplanar Konishi Anomalies and Effective Superpotential for Noncommutative N=1 Supersymmetric U(1)
• High-Energy Scattering in Non-Commutative Field Theory