### Abstract

We study the gauge anomaly A defined on a 4-dimensional infinite lattice while keeping the lattice spacing finite. We assume that (I) A depends smoothly and locally on the gauge potential, (II) A reproduces the gauge anomaly in the continuum theory in the classical continuum limit, and (III) U(1) gauge anomalies have a topological property. It is then shown that the gauge anomaly A can always be removed by local counterterms to all orders in powers of the gauge potential, leaving possible breakings proportional to the anomaly in the continuum theory. This follows from an analysis of nontrivial local solutions to the Wess-Zumino consistency condition in lattice gauge theory. Our result is applicable to the lattice chiral gauge theory based on the Ginsparg-Wilson Dirac operator, when the gauge field is sufficiently weak ∥U(n,μ)-1∥<ε′ , where U(n,μ) is the link variable and ε′ a certain small positive constant.

Original language | English |
---|---|

Pages (from-to) | 471-513 |

Number of pages | 43 |

Journal | Nuclear Physics B |

Volume | 585 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - Oct 2 2000 |

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### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics B*,

*585*(1-2), 471-513. https://doi.org/10.1016/S0550-3213(00)00408-9

**Anomaly cancellation condition in lattice gauge theory.** / Suzuki, Hiroshi.

Research output: Contribution to journal › Article

*Nuclear Physics B*, vol. 585, no. 1-2, pp. 471-513. https://doi.org/10.1016/S0550-3213(00)00408-9

}

TY - JOUR

T1 - Anomaly cancellation condition in lattice gauge theory

AU - Suzuki, Hiroshi

PY - 2000/10/2

Y1 - 2000/10/2

N2 - We study the gauge anomaly A defined on a 4-dimensional infinite lattice while keeping the lattice spacing finite. We assume that (I) A depends smoothly and locally on the gauge potential, (II) A reproduces the gauge anomaly in the continuum theory in the classical continuum limit, and (III) U(1) gauge anomalies have a topological property. It is then shown that the gauge anomaly A can always be removed by local counterterms to all orders in powers of the gauge potential, leaving possible breakings proportional to the anomaly in the continuum theory. This follows from an analysis of nontrivial local solutions to the Wess-Zumino consistency condition in lattice gauge theory. Our result is applicable to the lattice chiral gauge theory based on the Ginsparg-Wilson Dirac operator, when the gauge field is sufficiently weak ∥U(n,μ)-1∥<ε′ , where U(n,μ) is the link variable and ε′ a certain small positive constant.

AB - We study the gauge anomaly A defined on a 4-dimensional infinite lattice while keeping the lattice spacing finite. We assume that (I) A depends smoothly and locally on the gauge potential, (II) A reproduces the gauge anomaly in the continuum theory in the classical continuum limit, and (III) U(1) gauge anomalies have a topological property. It is then shown that the gauge anomaly A can always be removed by local counterterms to all orders in powers of the gauge potential, leaving possible breakings proportional to the anomaly in the continuum theory. This follows from an analysis of nontrivial local solutions to the Wess-Zumino consistency condition in lattice gauge theory. Our result is applicable to the lattice chiral gauge theory based on the Ginsparg-Wilson Dirac operator, when the gauge field is sufficiently weak ∥U(n,μ)-1∥<ε′ , where U(n,μ) is the link variable and ε′ a certain small positive constant.

UR - http://www.scopus.com/inward/record.url?scp=0000399917&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000399917&partnerID=8YFLogxK

U2 - 10.1016/S0550-3213(00)00408-9

DO - 10.1016/S0550-3213(00)00408-9

M3 - Article

AN - SCOPUS:0000399917

VL - 585

SP - 471

EP - 513

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 1-2

ER -