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This research aims to establish a mathematical connection between the index of Dirac operators on toroidal geometries and K-theory.

The index of lattice Dirac operators and K-theory

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This research aims to establish a mathematical connection between the index of Dirac operators on toroidal geometries and K-theory.
Prove equality between the index of a continuum Dirac operator and the eta invariant of a Wilson Dirac operator.
Utilize K-theory to formulate findings without relying on modified chiral symmetry.
Evaluate the indices through spectral flow and the eta invariant at finite mass.
The index of the continuum Dirac operator and the eta invariant of the lattice operator are shown to be equal.
A one-parameter family of continuum massive Dirac operators and their lattice counterparts belong to the same K^1 equivalence class at finite lattice spacing.

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Mathematical analysis reveals an equality between index of continuum and lattice Dirac operators, highlighting K-theory's utility.

Aoki et al. (2026) studied this question.

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