A numerical test of the continuum index theorem on the lattice

Abstract

The overlap formalism of chiral fermions provides a tool to measure the index, Q, of the chiral Dirac operator in a fixed gauge field background on the lattice. This enables a numerical measurement of the probability distribution, p(Q), in Yang-Mills theories. We have obtained an estimate for p(Q) in pure SU(2) gauge theory by measuring Q on 140 independent gauge field configurations generated on a 12^4 lattice using the standard single plaquette Wilson action at a coupling of beta=2.4. This distribution is in good agreement with a recent measurement [8] of the distribution of the topological charge on the same lattice using the same coupling and the same lattice gauge action. In particular we find <Q^2>=3.3(4) to be compared with <Q^2> = 3.9(5) found in [8]. The good agreement between the two distributions is an indication that the continuum index theorem can be carried over in a probabilistic sense on to the lattice.

17 pages, 5 figures, plain TeX, uses epsf

Cited by in corpus (41)

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• Quenched Lattice QCD with Domain Wall Fermions and the Chiral Limit
• Weak coupling expansion of massless QCD with a Ginsparg-Wilson fermion and axial U(1) anomaly
• Spectral flow, condensate and topology in lattice QCD
• Super Yang-Mills on the lattice with domain wall fermions
• Topological Charge and The Spectrum of Exactly Massless Fermions on the Lattice
• Gap Domain Wall Fermions
• The hermitian Wilson-Dirac operator in smooth SU(2) instanton backgrounds
• The finite temperature QCD phase transition with domain wall fermions
• Topology, fermionic zero modes and flavor singlet correlators in finite temperature QCD
• On the continuum limit of fermionic topological charge in lattice gauge theory
• Exact Chiral Symmetry on the Lattice
• Topological susceptibility from the overlap
• Domain wall fermions in vector gauge theories
• Quark mass effects on the topological susceptibility in QCD
• Lattice QCD Thermodynamics with Physical Quark Masses
• Topology and chiral symmetry breaking in SU(N) gauge theories
• A critical comparison of different definitions of topological charge on the lattice
• Domain wall fermions and applications
• On the spectrum of the Wilson-Dirac lattice operator in topologically non-trivial background configurations
• The Euclidean two-point correlation function of the topological charge density
• Overlap formula for the chiral multiplet
• The index of the overlap Dirac operator on a discretized 2d non-commutative torus
• Clover improvement, spectrum and Atiyah-Singer index theorem for the Dirac operator on the lattice
• SU(2) Gluodynamics and HP1 sigma-model embedding: Scaling, Topology and Confinement
• Wilson mass dependence of the overlap topological charge density
• Ginsparg-Wilson Fermions: A study in the Schwinger Model
• Domain wall fermion zero modes on classical topological backgrounds
• More about the axial anomaly on the lattice
• Properties of the Fixed Point Lattice Dirac Operator in the Schwinger Model
• On the index theorem for Wilson fermions
• Confining string and its widening in HP1 embedding approach
• Remnant index theorem and low-lying eigenmodes for twisted mass fermions
• Lattice Gauge Fields Topology Uncovered by Quaternionic sigma-model Embedding
• Differential equation for spectral flows of hermitean Wilson-Dirac operator
• Smoothing algorithms for projected center-vortex gauge fields
• Proposal for Topologically Unquenched QCD
• Wess-Zumino-Witten term on the lattice
• The dependence of overlap topological charge density on Wilson mass parameter
• Analyzing the spectrum of general, non-hermitian Dirac operators
• Parity Conservation in Supersymmetric Vector-Like Theories