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The Index Theorem of Lattice Wilson–Dirac Operators via Higher Index Theory

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Abstract

We give a proof of the index theorem of lattice Wilson–Dirac operators, which states that the index of a twisted Dirac operator on the standard torus is described in terms of the corresponding lattice Wilson–Dirac operator. Our proof is based on the higher index theory of almost flat vector bundles.

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Acknowledgements

The author would like to thank Mikio Furuta for his inspiring seminar talk on the Wilson–Dirac operator at RIKEN. This work was supported by RIKEN iTHEMS and JSPS KAKENHI Grant Nos. 19K14544, JPMJCR19T2, 17H06461.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Shinshu University, 3-1-1 Asahi, Matsumoto, Nagano, 390-8621, Japan

    Yosuke Kubota

  2. iTHEMS Program, RIKEN, 2-1 Hirosawa, Wako, Saitama, 351-0198, Japan

    Yosuke Kubota

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  1. Yosuke Kubota
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Correspondence to Yosuke Kubota.

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Communicated by Karl-Henning Rehren.

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Kubota, Y. The Index Theorem of Lattice Wilson–Dirac Operators via Higher Index Theory. Ann. Henri Poincaré 23, 1297–1319 (2022). https://doi.org/10.1007/s00023-022-01159-z

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  • DOI: https://doi.org/10.1007/s00023-022-01159-z

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