Quark Numbers and Percolation in QCD

Abstract

In this thesis, we are concerned with Lattice QCD and present two results. First, we construct an ensemble where the baryon number is fixed to fractional values in a spatial subvolume V. Due to gauge invariance and the implied Gauss law, the baryon number cannot be fixed to a fractional value on the whole periodic volume because any state with a net-quark number which is not a multiple of three has additional quarks or antiquarks whose color-electric fluxes cannot terminate in a gauge-invariant manner. For a subvolume V, this restriction does not apply. The fluxes can terminate at corresponding charges outside of V. However, the interaction has to be modified at the surface of V to make the system aware of the arbitrarily chosen subvolume. This is done with two independent approaches: a quantum-mechanical description of Lattice QCD and a dual formulation of the path integral. Second, we investigate the phenomenon of percolation as a mechanism for confinement. To this end, we base our considerations on a suggestion by Satz to describe the transition between confinement and deconfinement by a percolation transition. Similar to the Kertész line of spin systems, the percolation transition then coincides with the notion of confinement based on the spontaneous breaking of the Z3 symmetry at infinite quark masses but persists at light masses. This allows for an unambiguous distinction between a confined and deconfined phase at all parameters of the theory. We propose the correct mechanism to be given by the percolation of center-electric fluxes, define the spanning probability, derive the path integral and show that the confinement transition at infinite quark masses can be seen as a consequence of our notion of percolation. As a proof of concept, we demonstrate both main results numerically in a simple flux-tube model which shares the necessary center-electric flux structures with QCD.