The potential of the effective Polyakov line action from the underlying lattice gauge theory

I adapt a numerical method, previously applied to investigate the Yang-Mills vacuum wavefunctional, to the problem of extracting the effective Polyakov line action from SU(N) lattice gauge theories, with or without matter fields. The method can be used to find the variation of the effective Polyakov line action along any trajectory in field configuration space; this information is sufficient to determine the potential term in the action, and strongly constrains the possible form of the kinetic term. The technique is illustrated for both pure and gauge-Higgs SU(2) lattice gauge theory at finite temperature. A surprise, in the pure gauge theory, is that the potential of the corresponding Polyakov line action contains a non-analytic (yet center-symmetric) term proportional to |P|^3, where P is the trace of the Polyakov line at a given point, in addition to the expected analytic terms proportional to even powers of P.Comment: 24 pages, 12 figure

Confinement from Center Vortices: A review of old and new results

I briefly review the numerical evidence, some old and some quite recent, in favor of the center vortex theory of confinement.Comment: Invited talk at the Confinement 12 meeting, Thessaloniki, Greece, Aug. 2016. 12 pages, 8 figure

Scaling properties of Wilson loops pierced by P-vortices

P-vortices, in an SU(N) lattice gauge theory, are excitations on the center-projected Z(N) lattice. We study the ratio of expectation values of SU(2) Wilson loops, on the unprojected lattice, linked to a single P-vortex, to that of Wilson loops which are not linked to any P-vortices. When these ratios are plotted versus loop area in physical units, for a range of lattice couplings, it is found that the points fall approximately on a single curve, consistent with scaling. We also find that the ratios are rather insensitive to the point where the minimal area of the loop is pierced by the P-vortex.Comment: 4 pages, 4 figure