Numerical study of lattice index theorem usingimproved cooling and overlap fermions

Abstract

We investigate topological charge and the index theorem on finite lattices numerically. Using mean field improved gauge field configurations we calculate the topological charge Q using the gluon field definition with $\mathcal{O}(a^4)$-improved cooling and an $\mathcal{O}(a^4)$-improved field strength tensor $F_{\mu \nu }$. We also calculate the index of the massless overlap fermion operator by directly measuring the differences of the numbers of zero modes with left- and right--handed chiralities. For sufficiently smooth field configurations we find that the gluon field definition of the topological charge is integer to better than 1% and furthermore that this agrees with the index of the overlap Dirac operator, i.e., the Atiyah-Singer index theorem is satisfied. This establishes a benchmark for reliability when calculating lattice quantities which are very sensitive to topology.

15 pages, 1 figures

Cited by in corpus (13)

• Theta dependence of SU(N) gauge theories in the presence of a topological term
• Highly-improved lattice field-strength tensor
• The Index Theorem and Universality Properties of the Low-lying Eigenvalues of Improved Staggered Quarks
• The Low-Lying Dirac Spectrum of Staggered Quarks
• Susceptibility of the QCD vacuum to CP-odd electromagnetic background fields
• Staggered fermions, zero modes, and flavor-singlet mesons
• Systematics of Staggered Fermion Spectral Properties and Topology
• The index of the overlap Dirac operator on a discretized 2d non-commutative torus
• Fractal dimension of the topological charge density distribution in SU(2) lattice gluodynamics
• Wilson mass dependence of the overlap topological charge density
• On the chirality of quark modes
• Lattice Gauge Fields Topology Uncovered by Quaternionic sigma-model Embedding
• The dependence of overlap topological charge density on Wilson mass parameter