In this paper we analyze the ground state of the heavy-quark qqqG system using standard principles of quark confinement and massive constituent gluons as established in the center-vortex picture. The known string tension K-F and approximately-known gluon mass M lead to a precise specification of the long-range nonrelativistic part of the potential binding the gluon to the quarks with no undetermined phenomenological parameters, in the limit of large interquark separation R. Our major tool (also used earlier by Simonov) is the use of proper-time methods to describe gluon propagation within the quark system, along with some elementary group theory describing the gluon Wilson-line as a composite of colocated q and (q) over bar lines. We show that (aside from color-Coulomb and similar terms) the gluon potential energy in the presence of quarks is accurately described (for small gluon fluctuations) via attaching these three strings to the gluon, which in equilibrium sits at the Steiner point of the Y-shaped string network joining the three quarks. The gluon undergoes small harmonic fluctuations that slightly stretch these strings and quasiconfine the gluon to the neighborhood of the Steiner point. To describe nonrelativistic ground-state gluonic fluctuations at large R we use the Schrodinger equation, ignoring mixing with l = 2 states. Available lattice data and real-world hybrids require consideration of R values small enough for significant relativistic corrections, which we apply using a variational principle for the relativistic harmonic-oscillator. We also consider the role of color-Coulomb contributions. In terms of interquark separations R, we find leading nonrelativistic large-R terms in the gluon excitation energy of the form epsilon(R) -> M + xi[K-F/(MR)](1/2) - zeta alpha(c)/R where xi, zeta are calculable numerical coefficients and alpha(c) similar or equal to 0.15 is the color-Coulomb q (q) over bar coupling. When the gluon is relativistic, epsilon similar to (K-F/R)(1/3). We get an acceptable fit to lattice data with M = 500 MeV. Although we do not consider it in full detail, we show that in the q (q) over barG hybrid the gluon is a bead that can slide without friction on a string joining the q and (q) over bar. We comment briefly on the significance of our findings to fluctuations of the minimal surface, a subject difficult to understand from the point of view of center vortices.

We offer a physicist's proof that center-vortex theory requires the area in the (quenched) Wilson-loop area law to involve an extremal area. This means that, unlike in string-theory-inspired models of confining flux tubes, area-law dynamics is determined by integrating over Wilson loops only, not over surface fluctuations for a fixed loop. Fluctuations leading to perimeter-law corrections come from loop fluctuations as well as integration over finite-thickness center-vortex collective coordinates. In d=3 (or d= 2 + 1) we exploit a contour form of the extremal area in isothermal (conformally flat metric on the surface) coordinates which is similar to d = 2 (or d = 1 + 1) QCD in many respects, except that there are both quartic and quadratic terms in the action. One major result is that at large angular momentum l in d= 3 + 1 the center-vortex extremal-area picture yields a linear Regge trajectory with a Regge slope-string tension product alpha'(0)K-F of 1/(2pi), which is the canonical Veneziano or string value. In a curious effect traceable to retardation, the quark kinetic terms in the action vanish relative to area-law terms in the large-l limit, in which light-quark masses similar toK(F)(1/2) are negligible. This corresponds to string-theoretic expectations, even though we emphasize that the extremal-area law is not a string theory quantum mechanically. We show how some quantum trajectory fluctuations as well as nonleading classical terms for finite mass yield corrections scaling with l(-1/2). We compare to old semiclassical calculations of relativistic (massless) q (q) over bar bound states at large l, which also yield asymptotically linear Regge trajectories, finding agreement with a naive string Picture (classically., not quantum mechanically) and disagreement with an effective-propagator model. We show that contour forms of the area law can be expressed in terms of Abelian gauge potentials, and we relate this to old work of Comtet.

In d=3 SU(N) gauge theory, we study a scalar-field theory model of center vortices, and their monopolelike companions called nexuses, that furnishes an approach to the determination of so-called k-string tensions. This model is constructed from stringlike quantum solitons introduced previously, and exploits the well-known relation between string partition functions and scalar-field theories in d=3. A basic feature of the model is that center vortices corresponding to magnetic flux J (in units of 2pi/N) are composites of J elementary J=1 constituent vortices that come in N-1 types, with repulsion between like constituents and attraction between unlike constituents. The scalar-field theory is of a somewhat unusual type, involving N scalar fields phi(i) (one of which is eliminated) that can merge, dissociate, and recombine while conserving flux modN. The properties of these fields are deduced directly from the corresponding gauge-theory quantum solitons. Every vacuum Feynman graph of the theory corresponds to a real-space configuration of center vortices. We use qualitative features of this theory based on the vortex action to study the problem of k-string tensions (explicitly at large N, although large N is in no way a restriction on the model in general), whose solution is far from obvious in center-vortex language. We construct a simplified dynamical picture of constituent-vortex merging, dissociation, and recombination, which allows in principle for the determination of vortex areal densities and k-string tensions. This picture involves pointlike molecules made of constituent atoms in d=2 which combine and disassociate dynamically. These molecules and atoms are cross sections of vortices piercing a test plane; the vortices evolve in a Euclidean "time" which is the location of the test plane along an axis perpendicular to the plane. A simple approximation to the molecular dynamics is compatible with k-string tensions that are linear in k for kmuch less thanN, as naively expected.

We correct an unfortunate error in an earlier work of the author, and show that in the center-vortex picture of QCD [gauge group SU(3)] the asymptotic quenched baryonic area law is the so-called Y law, described by a minimal area with three surfaces spanning the three quark world lines and meeting at a central Steiner line joining the two common meeting points of the world lines. (The earlier claim was that this area law was a so-called Delta law, involving three extremal areas spanning the three pairs of quark world lines.) By asymptotic we mean the Y law holds at asymptotically large quark separations from each other; at separations of the order of the gauge-theory scale length, there may be Delta-like contributions. We give a preliminary discussion of the extension of these results to SU(N),N>3. These results are based on the (correct) baryonic Stokes' theorem given in the earlier work claiming a Delta law. The Y-form area law for SU(3) is in agreement with the most recent lattice calculations.