Comments on Perturbative Dynamics of Non-Commutative Yang-Mills Theory

Abstract

We study the U(N) non-commutative Yang-Mills theory at the one-loop approximation. We check renormalizability and gauge invariance of the model and calculate the one-loop beta function. The interaction of the SU(N) gauge bosons with the U(1) gauge boson plays an important role in the consistency check. In particular, the SU(N) theory by itself is not consistent. We also find that the theta --> 0 limit of the U(N) theory does not converge to the ordinary SU(N) x U(1) commutative theory, even at the planar limit. Finally, we comment on the UV/IR mixing.

19 pages, Latex. 4 figures. v2: minor changes, refs. added. To appear in Nucl.Phys.B

References in corpus (6)

• String Theory and Noncommutative Geometry
• Perturbative analysis on infrared aspects of noncommutative QED on R^4
• Comments on Noncommutative Perturbative Dynamics
• Two-Loop Diagrams in Noncommutative ${\varphi }_4^4$ theory
• Chiral Gauge Anomalies on Noncommutative R^4
• A Note on Non-Commutative Orbifold Field Theories

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