Simple chromatic properties of gradient flow

Abstract

It has become customary to use a smoothing algorithm called "gradient flow" to fix the lattice spacing in a simulation, through a parameter called $t_0$. It is shown that in order to keep the length $t_0$ fixed with respect to mesonic or gluonic observables as the number of colors $N_c$ is varied, the fiducial point for the flow parameter must be scaled nearly linearly in $N_c$. In simulations with dynamical fermions, the dependence of $t_0$ on the pseudoscalar meson mass flattens as the number of colors rises, in a way which is consistent with large $N_c$ expectations.

13 pages, 5 figures, published version of paper

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• The equation of state in (2+1)-flavor QCD
• High-precision scale setting in lattice QCD
• Infinite N phase transitions in continuum Wilson loop operators
• SU(N) gauge theories at large N
• The topological susceptibility in the large-N limit of SU(N) Yang-Mills theory
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• Finite-temperature phase structure of SU(4) gauge theory with multiple fermion representations
• Short flow-time coefficients of CP-violating operators
• The Large $N_c$ limit of QCD on the lattice
• Stealth dark matter confinement transition and gravitational waves
• Topological susceptibility in QCD with two flavors and 3-5 colors -- a pilot study
• Reversibility Violation in the Hybrid Monte Carlo Algorithm
• The $\pi \pi$ scattering amplitude at large $N_{\text{c}}$
• Bulk-preventing actions for SU(N) gauge theories