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arXiv · 2205.06190

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

Claudio Bonanno·Massimo D'Elia·Biagio Lucini·Davide Vadacchino
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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 $\mathit{topological}\,\,\textit{freezing}$, 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 $\mathit{parallel}\,\,\mathit{tempering}\,\,\mathit{on}\,\,\mathit{boundary}\,\,\mathit{conditions}$ 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.

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Claudio Bonanno, Massimo D'Elia, Biagio Lucini, Davide Vadacchino. 2022-07-08. Towards glueball masses of large-$N$ $\mathrm{SU}(N)$ pure-gauge theories without topological freezing. https://doi.org/10.1016/j.physletb.2022.137281

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