The index of non-Hermitian Dirac operators that anticommute with a chirality operator is topologically protected when the operators are diagonalizable and elliptic.
The chiral torsional anomaly and the Nieh-Yan invariant with and without boundaries
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Atiyah--Singer Index Theorem for Non-Hermitian Dirac Operators
The index of non-Hermitian Dirac operators that anticommute with a chirality operator is topologically protected when the operators are diagonalizable and elliptic.