Topological Susceptibility under Gradient Flow

TL;DR

This paper investigates how the Gradient Flow affects topological susceptibility measurements in lattice field theories, comparing direct and slab methods across models like 2-flavour QCD and the 2d O(3) model.

Contribution

It provides a comparative analysis of topological susceptibility under Gradient Flow using different measurement techniques in multiple lattice models.

Findings

Methods yield consistent results for topological susceptibility.

Gradient Flow impacts the slab method differently in QCD and O(3) models.

Ongoing research on whether Gradient Flow leads to a finite continuum limit.

Abstract

We study the impact of the Gradient Flow on the topology in various models of lattice field theory. The topological susceptibility $\chi_{\rm t}$ is measured directly, and by the slab method, which is based on the topological content of sub-volumes ("slabs") and estimates $\chi_{\rm t}$ even when the system remains trapped in a fixed topological sector. The results obtained by both methods are essentially consistent, but the impact of the Gradient Flow on the characteristic quantity of the slab method seems to be different in 2-flavour QCD and in the 2d O(3) model. In the latter model, we further address the question whether or not the Gradient Flow leads to a finite continuum limit of the topological susceptibility (rescaled by the correlation length squared, $\xi^{2}$). This ongoing study is based on direct measurements of $\chi_{\rm t}$ in $L \times L$ lattices, at $L/\xi \simeq 6$.