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Standard local updating algorithms experience a critical slowing down closeto the continuum limit, which is particularly severe for topologicalobservables. In practice, the Markov chain tends to remain trapped in a fixedtopological sector. This problem further worsens at large $N$, and is known as$\mathit{topological}~\mathit{freezing}$. To mitigate it, we adopt the paralleltempering on boundary conditions proposed by M. Hasenbusch. This algorithmallows to obtain a reduction of the auto-correlation time of the topologicalcharge up to several orders of magnitude. With this strategy we are able toprovide the first computation of low-lying glueball masses at large $N$ free ofany systematics related to topological freezing.

Towards glueball masses of large-$N~\mathrm{SU}(N)$ Yang-Mills theories without topological freezing via parallel tempering on boundary conditions