Topological charge using cooling and the gradient flow

Abstract

The equivalence of cooling to the gradient flow when the cooling step $n_c$ and the continuous flow step of gradient flow $\tau$ are matched is generalized to gauge actions that include rectangular terms. By expanding the link variables up to subleading terms in perturbation theory, we relate $n_c$ and $\tau$ and show that the results for the topological charge become equivalent when rescaling $\tau \simeq n_c/(3-15c_1)$ where $c_1$ is the Symanzik coefficient multiplying the rectangular term. We, subsequently, apply cooling and the gradient flow using the Wilson, the Symanzik tree-level improved and the Iwasaki gauge actions to configurations produced with $N_f=2+1+1$ twisted mass fermions. We compute the topological charge, its distribution and the correlators between cooling and gradient flow at three values of the lattice spacing demonstrating that the perturbative rescaling $\tau \simeq n_c/(3-15c_1)$ leads to equivalent results.

21 pages, 10 figures

References in corpus (6)

• Perturbative analysis of the gradient flow in non-abelian gauge theories
• Light hadrons from lattice QCD with light (u,d), strange and charm dynamical quarks
• First Physics Results at the Physical Pion Mass from $N_f=2$ Wilson Twisted Mass Fermions at Maximal Twist
• Topological susceptibility and the sampling of field space in $N_f=2$ lattice QCD simulations
• Over-Improved Stout-Link Smearing
• Spectral density of the Dirac operator in two-flavour QCD

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