Topological susceptibility from the overlap

Abstract

The chiral symmetry at finite lattice spacing of Ginsparg-Wilson fermionic actions constrains the renormalization of the lattice operators; in particular, the topological susceptibility does not require any renormalization, when using a fermionic estimator to define the topological charge. Therefore, the overlap formalism appears as an appealing candidate to study the continuum limit of the topological susceptibility while keeping the systematic errors under theoretical control. We present results for the SU(3) pure gauge theory using the index of the overlap Dirac operator to study the topology of the gauge configurations. The topological charge is obtained from the zero modes of the overlap and using a new algorithm for the spectral flow analysis. A detailed comparison with cooling techniques is presented. Particular care is taken in assessing the systematic errors. Relatively high statistics (500 to 1000 independent configurations) yield an extrapolated continuum limit with errors that are comparable with other methods. Our current value from the overlap is $χ^{1/4} = 188 \pm 12 \pm 5 \MeV$.

18 pages, 7 figures

References in corpus (6)

• Numerical techniques for lattice QCD in the $\epsilon$--regime
• Lattice QCD in the epsilon-regime and random matrix theory
• Low-Dimensional Long-Range Topological Charge Structure in the QCD Vacuum
• Light quark masses, chiral condensate and quark-gluon condensate in quenched lattice QCD with exact chiral symmetry
• Spectral Properties of the Overlap Dirac Operator in QCD
• Exact Chiral Symmetry on the Lattice: QCD Applications

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• Low-energy couplings of QCD from topological zero-mode wave functions
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• Topological susceptibility from twisted mass fermions using spectral projectors and the gradient flow
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• Exploring Topology Conserving Gauge Actions for Lattice QCD
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• Wilson mass dependence of the overlap topological charge density
• Finite-size scaling for the left-current correlator with non-degenerate quark masses
• Probing the chiral weak Hamiltonian at finite volumes
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• Determination of the $\Delta S=1$ weak Hamiltonian in the SU(4) chiral limit through topological zero-mode wave functions
• Lattice Gauge Fields Topology Uncovered by Quaternionic sigma-model Embedding
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• Analysis of systematic errors in the calculation of renormalization constants of the topological susceptibility on the lattice
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