A first analysis of the ensemble of local maxima of maximal center gauge
arXiv:2301.05903 · doi:10.3390/universe9090389
Abstract
Maximal center gauge (MCG) aims to detect some of the most important vacuum configurations, suggesting thick magnetic flux tubes quantised to non-trivial center elements of the gauge group being responsible for confinement. Due to the NP-hardness of a global maximization of the gauge functional only numeric procedures aiming for local maxima are possible. We observe a linear decrease of the string tension with increasing gauge functional value of the local maxima. This implies that the request to get as close as possible to the absolute maximum is untainable. We compare global properties of the ensemble of local maxima with other methods to detect center vortices and with determinations of the string tension from full configurations. This comparison indicates that the information about the number and positions of center vortices is contained in the structure of the ensemble of local maxima. This may pave the way for a future more successful formulation of the gauge condition.
12 pages. Equations added and title modified
References in corpus (9)
- On the interrelation between monopoles, vortices, topological charge and chiral symmetry breaking: an analysis using overlap fermions for SU(2)
- Double-winding Wilson loops and monopole confinement mechanisms
- Intersections of thick Center Vortices, Dirac Eigenmodes and Fractional Topological Charge in SU(2) Lattice Gauge Theory
- A model of random center vortex lines in continuous 2+1-dimensional space-time
- The road to solving the Gribov problem of the center vortex model in quantum chromo dynamics
- Center regions as a solution to the Gribov problem of the center vortex model
- The ice-limit of Coulomb gauge Yang-Mills theory
- Constructing static quark-anti-quark creation operators from Laplacian eigenmodes
- The static energy of a quark-antiquark pair from Laplacian eigenmodes