Scale setting of SU($N$) Yang--Mills theory, topology and large-$N$ volume independence

Abstract

We set the scale of SU($N$) Yang--Mills theories for $N=3,5,8$ and in the large-$N$ limit via gradient flow, as a first step towards the computation of the large-$N$ $\Lambda$-parameter using step scaling. We adopt twisted boundary conditions to achieve large-$N$ volume reduction and the Parallel Tempering on Boundary Conditions algorithm to tame topological freezing. This setup allows accurate determinations of the gradient-flow scales down to lattice spacings as fine as $\sim 0.025$ fm for all the explored values of $N$, a regime that has never been reached with ergodic algorithms. Moreover, we are able to precisely estimate the finite-size systematics related to topological freezing, and to show the suppression of finite-volume effects expected by virtue of large-$N$ twisted volume reduction.

18 pages, 19 figures

References in corpus (20)

• High-precision scale setting in lattice QCD
• Infinite N phase transitions in continuum Wilson loop operators
• Critical slowing down and error analysis in lattice QCD simulations
• Finite volume QCD at fixed topological charge
• The anomalous magnetic moment of the muon in the Standard Model: an update
• SU(N) gauge theories in 3+1 dimensions: glueball spectrum, string tensions and topology
• Critical point and scale setting in SU(3) plasma: An update
• The topological susceptibility in the large-N limit of SU(N) Yang-Mills theory
• Fighting topological freezing in the two-dimensional CP${}^{N-1}$ model
• Towards glueball masses of large-$N$ $\mathrm{SU}(N)$ pure-gauge theories without topological freezing
• Testing volume independence of SU(N) pure gauge theories at large N
• Large-$N$ $SU(N)$ Yang-Mills theories with milder topological freezing
• The gradient flow running coupling with twisted boundary conditions
• Large-$N$ expansion and $\theta$-dependence of $2d$ $C{P}^{N-1}$ models beyond the leading order
• Power corrections from decoupling of the charm quark
• Volume independence for Yang-Mills fields on the twisted torus
• Scale setting for large-$N$ SUSY Yang-Mills on the lattice
• Lattice determination of the topological susceptibility slope ${\chi }^{\prime }$ of $2d{\mathrm{CP}}^{N-1}$ models at large $N$
• The twisted gradient flow coupling at one loop
• Machine-learned RG-improved gauge actions and classically perfect gradient flows