Index and overlap construction for staggered fermions

• Main Author: Adams, David H.
• Format: Article
• Published: 2011
• Subjects: DRNTU::Science::Physics::Nuclear and particle physics
• Online Access: https://hdl.handle.net/10356/94063; http://hdl.handle.net/10220/6935; http://pos.sissa.it/cgi-bin/reader/conf.cgi?confid=105
• Institution: Nanyang Technological University

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 [4]. 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 [6]. It seemed that, away from the continuum limit, the best one could have was a field-theoretic definition of the staggered fermion index [1]. 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