Topological susceptibility from the overlap

TL;DR

This paper uses the overlap formalism to accurately measure the topological susceptibility in SU(3) pure gauge theory, minimizing systematic errors and providing a reliable continuum limit estimate.

Contribution

It demonstrates the effectiveness of the overlap Dirac operator in calculating topological susceptibility with reduced systematic errors compared to traditional methods.

Findings

Topological susceptibility value: $oxed{188 ext{ MeV}}$ with controlled errors.

Overlap formalism provides a systematic error reduction in topological measurements.

Comparison with cooling techniques validates the overlap approach.

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 $\chi^{1/4} = 188 \pm 12 \pm 5 \MeV$.