### Abstract

We construct the Wess-Zumino-Witten (WZW) term in lattice gauge theory by using a Dirac operator which obeys the Ginsparg-Wilson relation. Topological properties of the WZW term known in the continuum are reproduced on the lattice as a consequence of a non-trivial topological structure of the space of admissible lattice gauge fields. In the course of this analysis, we observe that the gauge anomaly generally implies that there is no basis of a Weyl fermion which leads to a single-valued expectation value in the fermion sector. The lattice Witten term, which carries information of a gauge path along which the gauge anomaly is integrated, is separated from the WZW term and the multivaluedness of the Witten term is shown to be related to the homotopy group π_{2n+1}(G). We also discuss the global SU(2) anomaly on the basis of the WZW term.

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

Pages (from-to) | 317-342 |

Number of pages | 26 |

Journal | Journal of High Energy Physics |

Volume | 7 |

Issue number | 9 |

Publication status | Published - Sep 1 2003 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*7*(9), 317-342.

**Wess-Zumino-Witten term on the lattice.** / Fujiwara, Takanori; Suzuki, Hiroshi; Matsui, Kosuke; Yamamoto, Masaru.

Research output: Contribution to journal › Article

*Journal of High Energy Physics*, vol. 7, no. 9, pp. 317-342.

}

TY - JOUR

T1 - Wess-Zumino-Witten term on the lattice

AU - Fujiwara, Takanori

AU - Suzuki, Hiroshi

AU - Matsui, Kosuke

AU - Yamamoto, Masaru

PY - 2003/9/1

Y1 - 2003/9/1

N2 - We construct the Wess-Zumino-Witten (WZW) term in lattice gauge theory by using a Dirac operator which obeys the Ginsparg-Wilson relation. Topological properties of the WZW term known in the continuum are reproduced on the lattice as a consequence of a non-trivial topological structure of the space of admissible lattice gauge fields. In the course of this analysis, we observe that the gauge anomaly generally implies that there is no basis of a Weyl fermion which leads to a single-valued expectation value in the fermion sector. The lattice Witten term, which carries information of a gauge path along which the gauge anomaly is integrated, is separated from the WZW term and the multivaluedness of the Witten term is shown to be related to the homotopy group π2n+1(G). We also discuss the global SU(2) anomaly on the basis of the WZW term.

AB - We construct the Wess-Zumino-Witten (WZW) term in lattice gauge theory by using a Dirac operator which obeys the Ginsparg-Wilson relation. Topological properties of the WZW term known in the continuum are reproduced on the lattice as a consequence of a non-trivial topological structure of the space of admissible lattice gauge fields. In the course of this analysis, we observe that the gauge anomaly generally implies that there is no basis of a Weyl fermion which leads to a single-valued expectation value in the fermion sector. The lattice Witten term, which carries information of a gauge path along which the gauge anomaly is integrated, is separated from the WZW term and the multivaluedness of the Witten term is shown to be related to the homotopy group π2n+1(G). We also discuss the global SU(2) anomaly on the basis of the WZW term.

UR - http://www.scopus.com/inward/record.url?scp=23144451407&partnerID=8YFLogxK

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M3 - Article

AN - SCOPUS:23144451407

VL - 7

SP - 317

EP - 342

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 9

ER -