Non-parametric strings

A formulation to relate the free bosonic string to the geometry of the group of loops is discussed. A neat implementation of the quantum dynamics and the constraints is found in terms of contact loop deformations.     

Non-orientable strings

We describe the halfcomplex structure on non-orientable two-dimensional surfaces and calculate chiral determinants and Laplacians necessary for construction of the Polyakov measure.     

Stretching necklaces

Polyelectrolytes in poor solvents show a necklace structure where collapsed polymer pearls are linked to stretched strings. In the present paper the elasticity of such chains is studied in detail. Different deformation regimes are addressed. The first is the continuous regime, where many pearls are present. A continuous force extension relationship is calculated. The main contribution comes from the tension balance and the electrostatic repulsion of consecutive pearls. The main correction term stems from the finite size of the pearls, which monitors their surface energy. For a finite amount of pearls discontinuous stretching is predicted. Finally counterion effects are discussed qualitatively. Received 6 December 1999     

Non-archimedean strings

A full set of factorized, dual, crossing-symmetric tree-level N-point amplitudes is constructed for non-archimedean closed strings. Momentum components and space-time coordinates are still valued in the field of real numbers, quantum amplitudes in that of complex numbers. It is the world-sheet parameters, which one integrates over, that become p-adic. For the closed string the parameters are valued in quadratic extensions of the fields Q_p of p-adic numbers (p = prime).     

Superconducting strings

It is known that certain spontaneously broken gauge theories give rise to stable strings or vortex lines. In this paper it is shown that under certain conditions such strings behave like superconducting wires whose passage through astrophysical magnetic fields would generate a variety of striking and perhaps observable effects. The superconducting charge carriers may be either bosons (if a charged Higgs field has an expectation value in the core of the string) or fermions (if charged fermions are trapped in zero modes along the string, as is known to occur in certain circumstances). They might be observable as synchrotron sources or as sources of high-energy cosmic rays. If the charge carriers are ordinary quarks and leptons, the strings have important baryon number violating interactions with magnetic fields; such a string, traversing a galactic magnetic field of 10^?6 G, creates baryons (or antibaryons) at a rate of order 10¹² particles/cm of string per second.     

Relativisticp-branes without constraints and their relation to the wiggly extended objects

The invariant evolution parameter is often used in the formulation of a so-called unconstrained relativistic quantum theoryof a point particle. Such a theory is very elegant, and contains the usual Klein-Gordon or the Dirac particle as a special case. In the present paper we extend the unconstrained theory to describe a continuous set of point particles forming a string or, in general, a membrane of arbitrary dimension p.The action of this system is not invariant with respect to reparametrizations of the evolution parameter and therefore there is no constraints among the dynamical variables, and no need for ghosts in the quantized theory. Then we show that such an unconstrained membrane is equivalent to a wiggly membranewhich has variable tension on its (p+1)-dimensional worldsheet. The equations of motion admit the usual well-known Dirac-Nambu-Goto membranes as particular solutions.On leave from J. Stefan Institute, University of Ljubljana, 61111 Ljubljana, Slovenia.     

Fundamental cosmic strings

Cosmic strings are linear concentrations of energy that may be formed at phase transitions in the very early universe. At one time they were thought to provide a possible origin for the density inhomogeneities from which galaxies eventually develop, though this idea has been ruled out, primarily by observations of the cosmic microwave background (CMB). Fundamental strings are the supposed building blocks of all matter in superstring theory or its modern version, M-theory. These two concepts were originally very far apart, but recent developments have brought them closer. The ‘brane-world’ scenario in particular suggests the existence of macroscopic fundamental strings that could well play a role very similar to that of cosmic strings.

In this paper, we outline these new developments, and also analyse recent observational evidence, and prospects for the future.     

Little heterotic strings

We discuss toroidal orbifolds of the E ₈×E ₈ heterotic string, in which the free-fermionic Higgs–matter splitting is implemented by a shift in the internal lattice coupled with the fermion numbers of the gauge degrees of freedom. We consider models in which some choices of the orbifold result in the projection of the graviton. In the models that we consider the projection also results in flipping the spin–statistics assignments in the massive string spectrum, whereas the massless spectrum retains the conventional spin–statistics assignments. We argue that the partition functions are mathematically consistent for one- and multi-loop amplitudes, owning to the existence of supersymmetry in the spectrum. A duality between different models at non-zero temperature is briefly discussed.