Chiral Anomaly on Fuzzy 2-Sphere

Details Chiral Anomaly on Fuzzy 2-Sphere Chiral Anomaly on Fuzzy 2-Sphere

2002-09-17

arxiv.org/abs/hep-th/0209137v3

Phys.Rev. D67 (2003) 065018

Physics

High Energy Physics

High Energy Physics - Theory

latex 42 pages, references added, typo corrected, discussion added, the final version to appear in Phys.Rev.D

Scientific paper

10.1103/PhysRevD.67.065018

We investigate chiral anomaly for fermions in fundamental representation on noncommutative (fuzzy) 2-sphere. In spite that this system is realized by finite dimensional matrices and no regularization is necessary for either UV or IR, we can reproduce the correct chiral anomaly which is consistent with the calculations done in flat noncommutative space. Like the flat case, there are ambiguities to define chiral currents. We define chiral currents in a gauge-invariant way and a gauge-covariant way, and show that the corresponding anomalous chiral Ward-Takahashi identities take different forms. The Ward-Takahashi identity for the gauge-invariant current contains explicit nonlocality while that for the covariant one is given by a local expression.

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