Clover improvement, spectrum and Atiyah-Singer index theorem for the Dirac operator on the lattice

Details Clover improvement, spectrum and Atiyah-Singer index theorem for the Dirac operator on the lattice Clover improvement, spectrum and Atiyah-Singer index theorem for the Dirac operator on the lattice

1998-06-28

arxiv.org/abs/hep-lat/9806032v2

Nucl.Phys. B541 (1999) 305-319

Physics

High Energy Physics

High Energy Physics - Lattice

Revised version, to appear in Nucl. Phys. B; discussion reworded, References updated

Scientific paper

10.1016/S0550-3213(98)00826-8

We study the role of the O(a)-improving clover term for the spectrum of the lattice Dirac operator using cooled and thermalized SU(2) gauge field configurations. For cooled configurations we observe improvement of the spectral properties when adding the clover term. For the thermalized case (12^4, beta = 2.4) without clover term we find a rather bad separation of physical and doubler branches making a probabilistic interpretation of the Atiyah-Singer index theorem on the lattice questionable for this beta and lattice size. Adding the clover term leads to the creation of additional real eigenvalues which come in pairs of opposite chirality thus further worsening the situation for the index theorem.

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