Polyakov Loop Dynamics in the Center Symmetric Phase

A study of the center symmetric phase of SU(2) Yang Mills theory is presented. Realization of the center symmetry is shown to result from non-perturbative gauge fixing. Dictated by the center symmetry, this phase exhibits already at the perturbative level confinement like properties. The analysis is performed by investigating the dynamics of the Polyakov loops. The ultralocality of these degrees of freedom implies significant changes in the vacuum structure of the theory. General properties of the confined phase and of the transition to the deconfined phase are discussed. Perturbation theory built upon the vacuum of ultralocal Polyakov loops is presented and used to calculate, via the Polyakov loop correlator, the static quark-antiquark potential.Comment: 45 pages, LaTeX, 8 figure

Constructing the fermion-boson vertex in QED3

We derive perturbative constraints on the transverse part of the fermion-boson vertex in massive QED3 through its one loop evaluation in an arbitrary covariant gauge. Written in a particular form, these constraints naturally lead us to the first non-perturbative construction of the vertex, which is in complete agreement with its one loop expansion in all momentum regimes. Without affecting its one-loop perturbative properties, we also construct an effective vertex in such a way that the unknown functions defining it have no dependence on the angle between the incoming and outgoing fermion momenta. Such a vertex should be useful for the numerical study of dynamical chiral symmetry breaking, leading to more reliable results.Comment: 13 pages, 2 figure

Singular behaviour of the electromagnetic field

The singularities of the electromagnetic field are derived to include all the point-like multipoles representing an electric charge and current distribution. Firstly derived in the static case, the result is generalized to the dynamic one. We establish a simple procedure for passing from the first, to the second case.Comment: Latex, 21.pages, no figure

Anisotropic evolution of 5D Friedmann-Robertson-Walker spacetime

We examine the time evolution of the five-dimensional Einstein field equations subjected to a flat, anisotropic Robertson-Walker metric, where the 3D and higher-dimensional scale factors are allowed to dynamically evolve at different rates. By adopting equations of state relating the 3D and higher-dimensional pressures to the density, we obtain an exact expression relating the higher-dimensional scale factor to a function of the 3D scale factor. This relation allows us to write the Friedmann-Robertson-Walker field equations exclusively in terms of the 3D scale factor, thus yielding a set of 4D effective Friedmann-Robertson-Walker field equations. We examine the effective field equations in the general case and obtain an exact expression relating a function of the 3D scale factor to the time. This expression involves a hypergeometric function and cannot, in general, be inverted to yield an analytical expression for the 3D scale factor as a function of time. When the hypergeometric function is expanded for small and large arguments, we obtain a generalized treatment of the dynamical compactification scenario of Mohammedi [Phys.Rev.D 65, 104018 (2002)] and the 5D vacuum solution of Chodos and Detweiler [Phys.Rev.D 21, 2167 (1980)], respectively. By expanding the hypergeometric function near a branch point, we obtain the perturbative solution for the 3D scale factor in the small time regime. This solution exhibits accelerated expansion, which, remarkably, is independent of the value of the 4D equation of state parameter w. This early-time epoch of accelerated expansion arises naturally out of the anisotropic evolution of 5D spacetime when the pressure in the extra dimension is negative and offers a possible alternative to scalar field inflationary theory.Comment: 20 pages, 4 figures, paper format streamlined with main results emphasized and details pushed to appendixes, current version matches that of published versio

Correction Factors for Reactions involving Quark-Antiquark Annihilation or Production

In reactions with $q \bar q$ production or $q\bar q$ annihilation, initial- and final-state interactions give rise to large corrections to the lowest-order cross sections. We evaluate the correction factor first for low relative kinetic energies by studying the distortion of the relative wave function. We then follow the procedure of Schwinger to interpolate this result with the well-known perturbative QCD vertex correction factors at high energies, to obtain an explicit semi-empirical correction factor applicable to the whole range of energies. The correction factor predicts an enhancement for $q\bar q$ in color-singlet states and a suppression for color-octet states, the effect increasing as the relative velocity decreases. Consequences on dilepton production in the quark-gluon plasma, the Drell-Yan process, and heavy quark production processes are discussed.Comment: 25 pages (REVTeX), includes 2 uuencoded compressed postscript figure

Random matrix theory and QCD3QCD_3

We suggest that the spectral properties near zero virtuality of three dimensional QCD, follow from a Hermitean random matrix model. The exact spectral density is derived for this family of random matrix models both for even and odd number of fermions. New sum rules for the inverse powers of the eigenvalues of the Dirac operator are obtained. The issue of anomalies in random matrix theories is discussed.Comment: 10p., SUNY-NTG-94/1

't Hooft and Wilson loop ratios in the QCD plasma

The spatial 't Hooft loop measuring the electric flux and the spatial Wilsonloop measuring the magnetic flux are analyzed in hot SU(N) gauge theory. Both display area laws. On one hand the tension of the 't Hooft loop is perturbatively calculable, in the same sense as the pressure. We show that the O(g^3) contribution is absent. The ratio of multi-charged 't Hooft loops have a remarkably simple dependence on the charge, true up to, but not including, O(g^4). This dependence follows also from a simple model of free screened colour charges. On the other hand the surface tension of the Wilsonloop is non-perturbative. But in a model of screened free monopoles at very high temperature the known area law follows. The density of these monopoles starts to contribute to O(g^6) to the pressure. The ratio of the multicharged Wilson loops is calculable and identical to that of the 't Hooft loops.Comment: 28 pages, 8 figure

QCD Radiative Corrections to the Leptonic Decay Rate of the B_c Meson

The QCD radiative corrections to the leptonic decay rate of the $B_c$ meson are calculated using the formalism of nonrelativistic QCD (NRQCD) to separate short-distance and long-distance effects. The $B_c$ decay constant is factored into a sum of NRQCD matrix elements each multiplied by a short-distance coefficient. The short-distance coefficient for the leading matrix element is calculated to order $\alpha_s$ by matching a perturbative calculation in full QCD with the corresponding perturbative calculation in NRQCD. This short-distance correction decreases the leptonic decay rate by approximately $15\%$.Comment: Changed Eq. 2 to read 1/(8 \pi), put in a missing i M_{B_c} in Eq. 18, and put in a normalisation factor of 2 M_{B_c} in Eq. 19

Quarkonia and the Pole Mass

The pole mass of a heavy quark is ambiguous by an amount of order $\Lambda_{QCD}$. We show that the heavy-quark potential, $V(r)$, is similarly ambiguous, but that the total static energy, $2M_{pole}+V(r)$, is unambiguous when expressed in terms of a short-distance mass. This implies that the extraction of a short-distance mass from the quarkonium spectrum is free of an ambiguity of order $\Lambda_{QCD}$, in contrast with the pole mass.Comment: 6 pages, LateX. Minor revisions for publicatio

Stable gravastars with generalised exteriors

New spherically symmetric gravastar solutions, stable to radial perturbations, are found by utilising the construction of Visser and Wiltshire. The solutions possess an anti--de Sitter or de Sitter interior and a Schwarzschild--(anti)--de Sitter or Reissner--Nordstr\"{o}m exterior. We find a wide range of parameters which allow stable gravastar solutions, and present the different qualitative behaviours of the equation of state for these parameters.Comment: 14 pages, 11 figures, to appear in Classical and Quantum Gravit