Wess-Zumino-Witten term on the lattice

Takanori Fujiwara, Hiroshi Suzuki, Kosuke Matsui, Masaru Yamamoto

Research output: Contribution to journalArticle

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 π2n+1(G). We also discuss the global SU(2) anomaly on the basis of the WZW term.

Original languageEnglish
Pages (from-to)317-342
Number of pages26
JournalJournal of High Energy Physics
Volume7
Issue number9
Publication statusPublished - Sep 1 2003
Externally publishedYes

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anomalies
fermions
gauge theory
sectors
continuums
operators

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics

Cite this

Fujiwara, T., Suzuki, H., Matsui, K., & Yamamoto, M. (2003). Wess-Zumino-Witten term on the lattice. Journal of High Energy Physics, 7(9), 317-342.

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

In: Journal of High Energy Physics, Vol. 7, No. 9, 01.09.2003, p. 317-342.

Research output: Contribution to journalArticle

Fujiwara, T, Suzuki, H, Matsui, K & Yamamoto, M 2003, 'Wess-Zumino-Witten term on the lattice', Journal of High Energy Physics, vol. 7, no. 9, pp. 317-342.
Fujiwara T, Suzuki H, Matsui K, Yamamoto M. Wess-Zumino-Witten term on the lattice. Journal of High Energy Physics. 2003 Sep 1;7(9):317-342.
Fujiwara, Takanori ; Suzuki, Hiroshi ; Matsui, Kosuke ; Yamamoto, Masaru. / Wess-Zumino-Witten term on the lattice. In: Journal of High Energy Physics. 2003 ; Vol. 7, No. 9. pp. 317-342.
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