Influence of topology on the scale setting

Abstract

Recently a new method to set the scale in lattice gauge theories, based on the gradient flow generated by the Wilson action, has been proposed, and the systematic errors of the new scales t0 and w0 have been investigated by various groups. The Wilson flow provides also an interesting alternative smoothing procedure in particular useful for the measurement of the topological charge as a pure gluonic observable. We show the viability of this method for N=1 supersymmetric Yang-Mills theory by analysing the configurations produced by the DESY-Muenster collaboration. For increasing flow time the topological charge quickly approaches near-integer values. The topological susceptibility has been measured for different fermion masses and its value is observed to approach zero in the chiral limit. Finally, the relation between the scale defined by the Wilson flow and the topological charge has been investigated, demonstrating a correlation between these two quantities.

17 pages, 12 figures

References in corpus (11)

• High-precision scale setting in lattice QCD
• Infinite N phase transitions in continuum Wilson loop operators
• Finite volume QCD at fixed topological charge
• Comparison of the gradient flow with cooling in $SU(3)$ pure gauge theory
• Two-flavor QCD simulation with exact chiral symmetry
• Simulation of 4d N=1 supersymmetric Yang-Mills theory with Symanzik improved gauge action and stout smearing
• The mass of the adjoint pion in N=1 supersymmetric Yang-Mills theory
• Non-renormalizability of the HMC algorithm
• Scale setting in lattice QCD
• Anomalies, gauge field topology, and the lattice
• Latest lattice results of N=1 supersymmetric Yang-Mills theory with some topological insights

Cited by in corpus (13)

• The light bound states of supersymmetric SU(2) Yang-Mills theory
• The light bound states of $\mathcal{N}=1$ supersymmetric SU(3) Yang-Mills theory on the lattice
• Numerical results for the lightest bound states in $\mathcal{N}=1$ supersymmetric SU(3) Yang-Mills theory
• Progress and prospects of lattice supersymmetry
• Lattice studies of supersymmetric gauge theories
• Improved thermodynamics of SU(2) gauge theory
• Background field method in the gradient flow
• Lattice simulations of a gauge theory with mixed adjoint-fundamental matter
• Investigating the conformal behaviour of SU(2) with one adjoint Dirac flavor
• The running coupling from gluon and ghost propagators in the Landau gauge: Yang-Mills theories with adjoint fermions
• Variational analysis of low-lying states in supersymmetric Yang-Mills theory
• Monte-Carlo simulations of overlap Majorana fermions
• Supermultiplets of the N=1 supersymmetric Yang-Mills theory in the continuum limit