Towards glueball masses of large-$N$ $\mathrm{SU}(N)$ pure-gauge theories without topological freezing

Abstract

In commonly used Monte Carlo algorithms for lattice gauge theories the integrated autocorrelation time of the topological charge is known to be exponentially-growing as the continuum limit is approached. This $topological\text{freezing}$, whose severity increases with the size of the gauge group, can result in potentially large systematics. To provide a direct quantification of the latter, we focus on $\mathrm{SU}(6)$ Yang--Mills theory at a lattice spacing for which conventional methods associated to the decorrelation of the topological charge have an unbearable computational cost. We adopt the recently proposed $paralleltemperingonboundaryconditions$ algorithm, which has been shown to remove systematic effects related to topological freezing, and compute glueball masses with a typical accuracy of $2-5\%$. We observe no sizeable systematic effect in the mass of the first lowest-lying glueball states, with respect to calculations performed at nearly-frozen topological sector.

16 pages, 8 eps figures, revised version matches published one

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• $Sp(2N)$ 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 $N$
• Thermodynamics of the Glueball Resonance Gas
• Topological susceptibility of $2d{\mathrm{CP}}^1$ or $\mathrm{O}(3)$ non-linear $\sigma$-model: is it divergent or not?
• Is $f_2(1950)$ the tensor glueball?
• 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