Index and overlap construction for staggered fermions.
Adams, David H.
Date of Issue2010
Staggered fermions had long been perceived as disadvantaged compared to Wilson fermions regarding the index theorem connection between (would-be) zero-modes and gauge field topology. For Wilson fermions, the would-be zero-modes can be identified as eigenmodes with low-lying real eigenvalues; these can be assigned chirality ±1 according to the sign of y¯ g5y, thereby determining an integer-valued index which coincides with the topological charge of the background lattice gauge field in accordance with the index theorem when the gauge field is not too rough [1, 2, 3]. It coincides with the index obtained from the exact chiral zero-modes of the overlap Dirac operator . In contrast, for staggered fermions, no way to identify the would-be zero-modes was known. They appeared to be mixed in with the other low-lying modes (all having purely imaginary eigenvalues) [1, 5] and only separating out close to the continuum limit . It seemed that, away from the continuum limit, the best one could have was a field-theoretic definition of the staggered fermion index . The latter had the disadvantages of being non-integer, requiring a renormalization depending on the whole ensemble of lattice gauge fields, and being significantly less capable than the Wilson fermion index of maintaining the index theorem in rougher backgrounds
DRNTU::Science::Physics::Nuclear and particle physics
The XXVIII international symposium on lattice field theory
© 2011 The Author.