### Abstract

We study the axial anomaly defined on a finite-size lattice by using a Dirac operator which obeys the Ginsparg-Wilson relation. When the gauge group is U(1), we show that the basic structure of axial anomaly on the infinite lattice, which can be deduced by a cohomological analysis, persists even on (sufficiently large) finite-size lattices. For non-Abelian gauge groups, we propose a conjecture on a possible form of axial anomaly on the infinite lattice, which holds to all orders in perturbation theory. With this conjecture, we show that a structure of the axial anomaly on finite-size lattices is again basically identical to that on the infinite lattice. Our analysis with the Ginsparg-Wilson-Dirac operator indicates that, in appropriate frameworks, the basic structure of axial anomaly is quite robust and it persists even in a system with finite ultraviolet and infrared cutoffs.

Original language | English |
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Pages (from-to) | 383-394 |

Number of pages | 12 |

Journal | Nuclear Physics B |

Volume | 644 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - Nov 11 2002 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics B*,

*644*(1-2), 383-394. https://doi.org/10.1016/S0550-3213(02)00812-X