On the continuum limit of fermionic topological charge in lattice gauge theory

Abstract

It is proved that the fermionic topological charge of SU(N) lattice gauge fields on the 4-torus, given in terms of a spectral flow of the Hermitian Wilson--Dirac operator, or equivalently, as the index of the Overlap Dirac operator, reduces to the continuum topological charge in the classical continuum limit when the parameter $m_0$ is in the physical region $0<m_0<2$.

latex, 18 pages. v2: Several comments added. To appear in J.Math.Phys

References in corpus (1)

• Bounds on the Wilson Dirac Operator

Cited by in corpus (29)

• The U_A(1) Problem on the Lattice with Ginsparg-Wilson Fermions
• Proposal for the numerical solution of planar QCD
• Accelerated Overlap Fermions
• Index Theorem and Overlap Formalism with Naive and Minimally Doubled Fermions
• Topology and higher dimensional representations
• On the consistency of the Aoki-phase
• The topological structure of SU(2) gluodynamics at T > 0 : an analysis using the Symanzik action and Neuberger overlap fermions
• Axial anomaly with the overlap-Dirac operator in arbitrary dimensions
• Tests of the lattice index theorem
• The index of the overlap Dirac operator on a discretized 2d non-commutative torus
• The rooting issue for a lattice fermion formulation similar to staggered fermions but without taste mixing
• Gauge fixing, families index theory, and topological features of the space of lattice gauge fields
• Wilson mass dependence of the overlap topological charge density
• Numerical study of lattice index theorem usingimproved cooling and overlap fermions
• Classical Limits of Scalar and Tensor Gauge Operators Based on the Overlap Dirac Matrix
• More about the axial anomaly on the lattice
• General bounds on the Wilson-Dirac operator
• Families index theory for Overlap lattice Dirac operator. I
• Quark masses, the Dashen phase, and gauge field topology
• Axial Anomaly and Index of the Overlap Hypercube Operator
• A renormalisation group derivation of the overlap formulation
• Canonical Approach to Ginsparg-Wilson Fermion
• Parity Realization in Lattice QCD with Ginsparg-Wilson Fermions
• A lattice version of the Atiyah-Singer index theorem
• Axial anomaly in the reduced model: Higher representations
• Combining the color structures and intersection points of thick center vortices and low-lying Dirac modes
• Wess-Zumino-Witten term on the lattice
• Fractional topological charges and the lowest Dirac modes
• Fermionic topological charge of families of lattice gauge fields