UV/IR Mixing and Anomalies in Noncommutative Gauge Theories

Abstract

Using path integral method (Fujikawa's method) we calculate anomalies in noncommutative gauge theories with fermions in the bi-fundamental and adjoint representations. We find that axial and chiral gauge anomalies coming from non-planar contributions are derived in the low noncommutative momentum limit ${\tilde{p}}^{\mu }(\equiv {\theta }^{\mu \nu }{p}_{\nu })\to 0$. The adjoint chiral fermion carries no anomaly in the non-planar sector in $D=4k(k=1,2,...,)$ dimensions. It is naturally shown from the path integral method that anomalies in non-planar sector originate in UV/IR mixing.

15 pages, no figures, LaTeX, minor corrections and references added

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• Bosonized noncommutative bi-fundamental fermion and S-duality
• Non-commutative solitons and strong-weak duality
• The U(1)A anomaly in noncommutative SU(N) theories
• Gravitational Anomalies in Noncommutative Field Theory