General bounds on the Wilson-Dirac operator

Abstract

Lower bounds on the magnitude of the spectrum of the Hermitian Wilson-Dirac operator H(m) have previously been derived for 0<m<2 when the lattice gauge field satisfies a certain smoothness condition. In this paper lower bounds are derived for 2p-2<m<2p for general p=1,2,...,d where d is the spacetime dimension. The bounds can alternatively be viewed as localisation bounds on the real spectrum of the usual Wilson-Dirac operator. They are needed for the rigorous evaluation of the classical continuum limit of the axial anomaly and index of the overlap Dirac operator at general values of m, and provide information on the topological phase structure of overlap fermions. They are also useful for understanding the instanton size-dependence of the real spectrum of the Wilson-Dirac operator in an instanton background.

26 pages, 2 figures. v3: Completely rewritten with new material and new title; to appear in Phys.Rev.D

References in corpus (7)

• Bounds on the Wilson Dirac Operator
• Algebraic Generalization of the Ginsparg-Wilson Relation
• On the continuum limit of fermionic topological charge in lattice gauge theory
• Axial anomaly with the overlap-Dirac operator in arbitrary dimensions
• A Primer on Instantons in QCD
• Locality Properties of a New Class of Lattice Dirac Operators
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Cited by in corpus (9)

• Theoretical foundation for the Index Theorem on the lattice with staggered fermions
• Filtered overlap: speedup, locality, kernel non-normality and Z_A~1
• Topology and higher dimensional representations
• Generalising the Ginsparg-Wilson relation: Lattice Supersymmetry from Blocking Transformations
• The rooting issue for a lattice fermion formulation similar to staggered fermions but without taste mixing
• Blocking-inspired supersymmetric actions: a status report
• Numerical indication that center vortices drive dynamical mass generation in QCD
• Smoothing algorithms for projected center-vortex gauge fields
• Improving the locality of the overlap Dirac operator via approximate solutions of the Ginsparg-Wilson relation