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arXiv · hep-th/0211164

The Gauge Anomaly and the Seiberg-Witten Map

C. P. Martin
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Abstract

The consistent form of the gauge anomaly is worked out at first order in $θ$ for the noncommutative three-point function of the ordinary gauge field of certain noncommutative chiral gauge theories defined by means of the Seiberg-Witten map. We obtain that for any compact simple Lie group the anomaly cancellation condition of this three-point function reads $\traza \T^a \T^b \T^c = 0$, if one restricts the type of noncommutative counterterms that can be added to the classical action to restore the gauge symmetry to those which are renormalizable by power-counting. On the other hand, if the power-counting remormalizability paradigm is relinquished and one admits noncommutative counterterms (of the gauge fields, its derivatives and $θ$) which are not power-counting renormalizable, then, the anomaly cancellation condition for the noncommutative three-point function of the ordinary gauge field becomes the ordinary one: $\traza \T^a \{\T^b,\T^c\} = 0$.

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C. P. Martin. 2002-11-19. The Gauge Anomaly and the Seiberg-Witten Map. https://doi.org/10.1016/s0550-3213(03)00037-3

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