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Index theorem with minimally doubled fermions in four spacetime dimensions

Abhijeet Kishore1,*, Subhasish Basak2,†, and Dipankar Chakrabarti1,‡

  • *Contact author: akishore@iitk.ac.in
  • †Contact author: sbasak@niser.ac.in
  • ‡Contact author: dipankar@iitk.ac.in
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Phys. Rev. D 113, 114511 – Published 11 June, 2026

DOI: https://doi.org/10.1103/d5f8-p5hs

Abstract

We determine the zero eigenmode spectrum of minimally doubled fermions, namely in Karsten-Wilczek and Borici-Creutz formulations on the four-dimensional spacetime lattice. We employ background gauge fields with integer valued topological charges. The Atiyah-Singer Index Theorem is verified in the presence of two different background gauge fields, namely Smit-Vink [1] and cooled down MILC asqtad ensembles with Nf=2+1 dynamical flavors of quarks [2]. Using flavored mass terms [3,4], we find that the spectral flow of the eigenvalues detects the topology of the background gauge field. With the use of the modified chirality operator, we obtain chiralities of the zero eigenmodes and the fermionic topological charge.

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Phys. Rev. D 113, 114511– Published 11 June, 2026
  • Received 27 February 2026
  • Accepted 27 April 2026
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