Large-$N$ $SU(N)$ Yang-Mills theories with milder topological freezing

Abstract

We simulate $4d$ $SU(N)$ pure-gauge theories at large $N$ using a parallel tempering scheme that combines simulations with open and periodic boundary conditions, implementing the algorithm originally proposed by Martin Hasenbusch for $2d$ $C{P}^{N-1}$ models. That allows to dramatically suppress the topological freezing suffered from standard local algorithms, reducing the autocorrelation time of $Q^2$ up to two orders of magnitude. Using this algorithm in combination with simulations at non-zero imaginary $\theta$ we are able to refine state-of-the-art results for the large-$N$ behavior of the quartic coefficient of the $\theta$-dependence of the vacuum energy $b_2$, reaching an accuracy comparable with that of the large-$N$ limit of the topological susceptibility.

11 pages, 9 eps figures, minor changes and few typos corrected

References in corpus (12)

• The glueball spectrum of SU(3) gauge theory in 3+1 dimension
• Theta dependence of the vacuum energy in the SU(3) gauge theory from the lattice
• $\theta$ dependence of 4D $SU(N)$ gauge theories in the large-$N$ limit
• 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
• Susceptibility of the QCD vacuum to CP-odd electromagnetic background fields
• Mass gap in the 2D O(3) non-linear sigma model with a theta=pi term
• Large-$N$ expansion and $\theta$-dependence of $2d$ $C{P}^{N-1}$ models beyond the leading order
• Behavior near $\theta =\pi$ of the mass gap in the 2D O(3) non-linear sigma model
• $\theta$-dependence and center symmetry in Yang-Mills theories
• Is $N=2$ Large?
• On the effective Lagrangian of CP^(N-1) models in the large N limit

Cited by in corpus (13)

• SU(N) gauge theories in 3+1 dimensions: glueball spectrum, string tensions and topology
• Phase Transitions in Particle Physics -- Results and Perspectives from Lattice Quantum Chromo-Dynamics
• Topological susceptibility of $N_f=2+1$ QCD from staggered fermions spectral projectors at high temperatures
• Topological sampling through windings
• Ergodic sampling of the topological charge using the density of states
• $Sp(2N)$ Yang-Mills theories on the lattice: scale setting and topology
• Lattice determination of the topological susceptibility slope ${\chi }^{\prime }$ of $2d{\mathrm{CP}}^{N-1}$ models at large $N$
• Fractional topological charge in $SU(N)$ gauge theories without dynamical quarks
• Topological susceptibility of $2d{\mathrm{CP}}^1$ or $\mathrm{O}(3)$ non-linear $\sigma$-model: is it divergent or not?
• Parallel Tempered Metadynamics: Overcoming potential barriers without surfing or tunneling
• Scaling of Stochastic Normalizing Flows in $\mathrm{SU}(3)$ lattice gauge theory
• Scaling flow-based approaches for topology sampling in $\mathrm{SU}(3)$ gauge theory
• Scale setting of SU($N$) Yang--Mills theory, topology and large-$N$ volume independence