Estimating \[\chi _\mathrm {top}\] lattice artifacts from flowed SU(2) calorons

Abstract

Lattice computations of the high-temperature topological susceptibility of QCD receive lattice-spacing corrections and suffer from systematics arising from the type and depth of gradient flow. We study the lattice spacing corrections to \[\chi _\mathrm {top}\] semi-analytically by exploring the behavior of discretized Harrington–Shepard calorons under the action of different forms of gradient flow. From our study we conclude that \[N_\tau = 6\] is definitely too small of a time extent to study the theory at temperatures of order \[4~T_\mathrm {c}\] and we explore how the amount of gradient flow influences the continuum extrapolation.