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Topological charge using cooling and the gradient flow
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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 $\tau \simeq n_c/({3-15 c_1})$ 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 $\tau \simeq n_c/({3-15 c_1})$ leads to equivalent results.
Forward citations
Cited by 6 Pith papers
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The topological susceptibility slope $\chi^\prime$ in the large-$N$ limit
First non-perturbative lattice determination of the Yang-Mills topological susceptibility slope χ' in the large-N limit using a novel algorithm to avoid topological freezing.
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Monte Carlo Simulation of the $SU(2)/\mathbb{Z}_2$ Yang--Mills Theory
Making the Z2 two-form gauge field dynamical in an SU(2)/Z2 lattice simulation shortens the autocorrelation time of the topological charge and of a gradient-flow energy observable compared with conventional SU(2) HMC.
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Scaling flow-based approaches for topology sampling in $\mathrm{SU}(3)$ gauge theory
Out-of-equilibrium simulations with open-to-periodic boundary switching plus a tailored stochastic normalizing flow enable efficient topology sampling in the continuum limit of four-dimensional SU(3) Yang-Mills theory.
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Topology via Spectral Projectors with Staggered Fermions
A staggered-fermion version of the spectral-projectors definition of topological charge is derived, generalized to all cumulants, and tested against gluonic and overlap results in pure SU(3).
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Lattice gradient flows (de-)stabilizing topological sectors
Iwasaki and DBW2 gradient flows keep the topological charge of SU(2) gauge configurations stable at long flow times, unlike Wilson and Symanzik flows; DBW2 quantizes the charge already near t=0.5.
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The imaginary-$\theta$ dependence of the SU($N$) spectrum
The theta-squared curvature of the SU(3) glueball mass and string tension is measured in the continuum, and the N=3 and N=6 data support the expected large-N 1/N^2 scaling.
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