  In d=3 SU(N) gauge theory, we study a scalar field theory model of center
vortices that furnishes an approach to the determination of so-called k-string
tensions. This model is constructed from string-like quantum solitons
introduced previously, and exploits the well-known relation between string
partition functions and scalar field theories in d=3. Center vortices
corresponding to magnetic flux J (in units of 2\pi /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 involves N scalar fields \phi_i (one of which is
eliminated) that can merge, dissociate, and recombine while conserving flux mod
N. 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 study
qualitatively the problem of k-string tensions at large N, 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 point-like "molecules" (cross-sections
of center vortices) made of constituent "atoms" that combine and disassociate
dynamically in a d=2 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 k<< N, as naively expected.
