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arXiv · hep-th/9602137

Anomalous Chiral Action from the Path-Integral

M. M. Islam·S. J. Puglia
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Abstract

By generalizing the Fujikawa approach, we show in the path-integral formalism: (1) how the infinitesimal variation of the fermion measure can be integrated to obtain the full anomalous chiral action; (2) how the action derived in this way can be identified as the Chern-Simons term in five dimensions, if the anomaly is consistent; (3) how the regularization can be carried out, so as to lead to the consistent anomaly and not to the covariant anomaly. Our method uses Schwinger's ``proper-time'' representation of the Green's function and the gauge invariant point-splitting technique. We find that the consistency requirement and the point-splitting technique allow both an anomalous and a non-anomalous action. In the end, the nature of the vacuum determines whether we have an anomalous theory, or, a non-anomalous theory

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M. M. Islam, S. J. Puglia. 1996-02-26. Anomalous Chiral Action from the Path-Integral. https://doi.org/10.1142/s0217751x98000226

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