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

TL;DR

This paper demonstrates that a novel parallel tempering algorithm effectively mitigates topological freezing in lattice gauge theory simulations, enabling accurate computation of glueball masses in large-$N$ SU(N) theories without systematic errors.

Contribution

The study introduces and applies a parallel tempering method to avoid topological freezing, allowing precise glueball mass calculations at large N without systematic biases.

Findings

No significant systematic effects on glueball masses due to topological freezing.

The method achieves 2-5% accuracy in mass measurements.

Effective for large gauge groups like SU(6).

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.