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

Abstract

Standard local updating algorithms experience a critical slowing down close to the continuum limit, which is particularly severe for topological observables. In practice, the Markov chain tends to remain trapped in a fixed topological sector. This problem further worsens at large N, and is known as topological freezing. To mitigate it, we adopt the parallel tempering on boundary conditions proposed by M. Hasenbusch. This algorithm allows to obtain a reduction of the auto-correlation time of the topological charge up to several orders of magnitude. With this strategy we are able to provide the first computation of low-lying glueball masses at large N free of any systematics related to topological freezing.