Abstract
In order to extract continuum properties, we study the topological charge density correlator (TCDC) and the inverse participation ratio (IPR) for the topological charge density in SU(3) lattice Yang-Mills theory for relatively small lattice spacings, including some smaller than those explored before. With the help of a recently proposed open boundary condition, it is possible to compute observables at a smaller lattice spacing since the trapping problem is absent. On the other hand, the reference energy scale provided by the Wilson flow allows us to study their scaling behavior, in contrast to previously proposed smearing techniques. The behavior of the TCDC for different lattice spacings at a fixed hypercubic smearing level shows apparent scaling violations. In contrast, at a particular Wilson flow time for all of the lattice spacings investigated (except the largest one), the TCDC data show universal behavior within our statistical uncertainties. The continuum properties of the TCDC are studied by investigating the small-flow-time behavior. We also extract the pseudoscalar glueball mass from the TCDC, which appears to be insensitive to the lattice spacings () and agrees with the value extracted using anisotropic lattices, within statistical errors. Further, we study the localization property of using the IPR (whose continuum behavior can be probed using small values of the Wilson flow time) and observe a decrease of the IPR with decreasing Wilson flow time. A detailed study of under the Wilson flow time reveals that as the Wilson flow time decreases, the proximity of the regions of positive and negative charge densities of large magnitude increases, and the charge density appears to be more delocalized, resulting in the observed behavior of the IPR.
7 More- Received 9 January 2015
DOI:https://doi.org/10.1103/PhysRevD.91.074507
© 2015 American Physical Society