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

Dynamical Origin of the Lorentzian Signature of Spacetime

It is suggested that not only the curvature, but also the signature of spacetime is subject to quantum fluctuations. A generalized D-dimensional spacetime metric of the form $g_{\mu \nu}=e^a_\mu \eta_{ab} e^b_\nu$ is introduced, where $\eta_{ab} = diag\{e^{i\theta},1,...,1\}$. The corresponding functional integral for quantized fields then interpolates from a Euclidean path integral in Euclidean space, at $\theta=0$, to a Feynman path integral in Minkowski space, at $\theta=\pi$. Treating the phase $e^{i\theta}$ as just another quantized field, the signature of spacetime is determined dynamically by its expectation value. The complex-valued effective potential $V(\theta)$ for the phase field, induced by massless fields at one-loop, is considered. It is argued that $Re[V(\theta)]$ is minimized and $Im[V(\theta)]$ is stationary, uniquely in D=4 dimensions, at $\theta=\pi$, which suggests a dynamical origin for the Lorentzian signature of spacetime.Comment: 6 pages, LaTe

Charge Screening, Large-N, and the Abelian Projection Model of Confinement

We point out that the abelian projection theory of quark confinement is in conflict with certain large-N predictions. According to both large-N and lattice strong-coupling arguments, the perimeter law behavior of adjoint Wilson loops at large scales is due to charge-screening, and is suppressed relative to the area term by a factor of $1/N^2$. In the abelian projection theory, however, the perimeter law is due to the fact that $N-1$ out of $N^2-1$ adjoint quark degrees of freedom are (abelian) neutral and unconfined; the suppression factor relative to the area law is thus only $1/N$. We study numerically the behavior of Wilson loops and Polyakov lines with insertions of (abelian) charge projection operators, in maximal abelian gauge. It appears from our data that the forces between abelian charged, and abelian neutral adjoint quarks are not significantly different. We also show via the lattice strong-coupling expansion that, at least at strong couplings, QCD flux tubes attract one another, whereas vortices in type II superconductors repel.Comment: 20 pages (Latex), 8 figures, IFUP-TH 54/9

Center Disorder in the 3D Georgi-Glashow Model

We present a number of arguments relating magnetic disorder to center disorder, in pure Yang-Mills theory in D=3 and D=4 dimensions. In the case of the D=3 Georgi-Glashow model, we point out that the abelian field distribution is not adequatedly represented, at very large scales, by that of a monopole Coulomb gas. The onset of center disorder is associated with the breakdown of the Coulomb gas approximation; this scale is pushed off to infinity in the QED_3 limit of the 3D Georgi-Glashow model, but should approach the color-screening length in the pure Yang-Mills limit.Comment: 22 pages including 3 figures, Latex2

Constituent Gluon Content of the Static Quark-Antiquark State in Coulomb Gauge

Motivated by the gluon-chain model of flux tube formation, we compute and diagonalize the transfer matrix in lattice SU(2) gauge theory for states containing heavy static quark-antiquark sources, with separations up to one fermi. The elements of the transfer matrix are calculated by variational Monte Carlo methods, in a basis of states obtained by acting on the vacuum state with zero, one, and two-gluon operators in Coulomb gauge. The color Coulomb potential is obtained from the zero gluon to zero gluon element of the transfer matrix, and it is well-known that while this potential is asymptotically linear, it has a slope which is two to three times larger than the standard asymptotic string tension. We show that the addition of one and two gluon states results in a potential which is still linear, but the disagreement with the standard asymptotic string tension is reduced to 38% at the largest lattice coupling we have studied