Topology and glueballs in SU(7) Yang-Mills with open boundary conditions

TL;DR

This paper investigates the impact of boundary conditions on topological properties and glueball correlations in SU(7) Yang-Mills theory, highlighting how open boundaries restore topological mobility at coarser lattices.

Contribution

It provides a comparative analysis of topological and glueball properties in SU(7) with periodic and open boundary conditions, emphasizing the effects on ergodicity and correlation functions.

Findings

Open boundary conditions improve topological mobility.

Topological charge fluctuations are enhanced with open boundaries.

Glueball correlators are affected by boundary conditions.

Abstract

It is well known that the topology of gauge configurations generated in a Markov Monte-Carlo chain freezes as the continuum limit is approached. The corresponding autocorrelation time increases exponentially with the inverse lattice spacing, affecting the ergodicity of the simulation. In SU(N) gauge theories for large N this problem sets in at much coarser lattice spacings than for N=3. This means that its systematics can be studied on lattices that are smaller in terms of the number of lattice sites. It has been shown that using open boundary conditions in time allows instantons to be created and destroyed, restoring topological mobility and ergodicity. However, with open boundary conditions translational invariance is lost and the influence of spurious states propagating from the boundary into the bulk on physical correlators needs to be carefully evaluated. Moreover, while the total topological charge can be changed, the mobility of instantons across the lattice is still reduced. We consider SU(7) Yang-Mills theory and analyse its topological content in the periodic and open boundary condition cases. We also investigate scalar and pseudo-scalar glueball correlation functions.