Seiberg Witten Map and the Axial Anomaly in Noncommutative Field Theory
arXiv:hep-th/0110177 · doi:10.1016/S0370-2693(02)01566-6
Abstract
Using the point-splitting regularisation, we calculate the axial anomaly in an arbitrary even dimensional Non-Commutative (NC) field theory. Our result is (star) gauge invariant in its {\it unintegrated} form, to the leading order in the NC parameter. Exploiting the Seiberg Witten map, this result gets transformed to the familiar Adler-Bell-Jackiw anomaly in ordinary space-time. Furthermore, using this map, we derive an expression for the unintegrated axial anomaly for constant fields in NC space-time, that is valid to all finite orders of the NC parameter.
Slightly modified version with minor changes in the reference, Jour. ref: Phys. Lett. B533 (2002) 162
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