New dimensions for old strings

A simple configuration of background fields is constructed to provide consistent string theories in arbitrary dimensions. The background solution involves a dilation field which is a linear function of the space-time coordinates. This background has a new instability apart from the presence of tachyons in the free spectrum.     

Unified field theories of bags and strings

Within our models of temporary quark confinement in field theoretical bags, we exhibit, in the tree approximation, string-like solutions. We argue that the bag-like and dual string-like pictures complement each other with the former describing the low-lying hadronic states and the latter the excited states of large angular momentum. When certain quantum fluctuation effects are included, we find Regge trajectories, in a certain dynamical regime, to always approach straight lines in a (J, E²) plane.     

Action functionals for strings in four dimensions

All possible action functionals on the space of surfaces in ⁴ that depend only on first and second derivatives of the functions, entering the equation of the surface, and satisfy the condition of invariance with respect to rigid motions, are described.     

Weyl fermions on strings embedded in three dimensions

It is shown that the determinant of the Weyl operator introduced by Kavalov, Kostov and Sedrakyan is determined by the extrinsic geometry of the embedding. The effective action is anomalous under bendings of the surface.     

A system of strings and springs in three dimensions

A three-dimensional array of classical strings and springs oscillating in three dimensions is investigated with combined analytical-numerical tools. The strings are continuous and linear. The long time behavior of the system changes dramatically when the springs are changed from linear to non-linear. The equipartition of energy, even among the particles, is badly violated. The power spectrum is consistent with chaotic motion. The maximal Lyapunov exponent is vanishing within our approximation. The most remarkable finding is a certain pairing of time averages for the particles, which occurs for many initial conditions in the non-linear case.     

Critical interface in two dimensions

The interface separating two-dimensional phases close to a critical point is observed in the ferroelectric BaZr_xTi_1−xO₃ by transmission electron microscopy. The temperature dependence of the interfacial thickness is determined and compared with theoretical predictions.     

Critical gravity in four dimensions

We study four-dimensional gravity theories that are rendered renormalizable by the inclusion of curvature-squared terms to the usual Einstein action with a cosmological constant. By choosing the parameters appropriately, the massive scalar mode can be eliminated and the massive spin-2 mode can become massless. This "critical" theory may be viewed as a four-dimensional analogue of chiral topologically massive gravity, or of critical "new massive gravity" with a cosmological constant, in three dimensions. We find that the on-shell energy for the remaining massless gravitons vanishes. There are also logarithmic spin-2 modes, which have positive energy. The mass and entropy of standard Schwarzschild-type black holes vanish. The critical theory might provide a consistent toy model for quantum gravity in four dimensions.     

Chern-Simons gauge theory on orbifolds: Open strings from three dimensions

Chern-Simons gauge theory is formulated on three-dimensional $\text{Z}$₂ orbifolds. The locus of singular points on a given orbifold is equivalent to a link of Wilson lines. This allows one to reduce any correlation function on orbifolds to a sum of more complicated correlation functions in the simpler theory on manifolds. Chern-Simons theory on manifolds is known to be related to two-dimensional (2D) conformal field theory (CFT) on closed-string surfaces; here it is shown that the theory on orbifolds is related to 2D CFT of unoriented closed- and open-string models, i.e. to worldsheet orbifold models. In particular, the boundary components of the worldsheet correspond to the components of the singular locus in the 3D orbifold. This correspondence leads to a simple identification of the open-string spectra, including their Chan-Paton degeneration, in terms of fusing Wilson lines in the corresponding Chern-Simons theory. The correspondence is studied in detail, and some exactly solvable examples are presented. Some of these examples indicate that it is natural to think of the orbifold group $\text{Z}$₂ as a part of the gauge group of the Chern-Simons theory, thus generalizing the standard definition of gauge theories.     

Critical dimensions of the diffusion equation

We study the evolution of a random initial field under pure diffusion in various space dimensions. From numerical calculations we find that the persistence properties of the system show sharp transitions at critical dimensions d(1) approximately 26 and d(2) approximately 46. We also give refined measurements of the persistence exponents for low dimensions.     

Critical dimensions for YBCO islands grown by pulsed laser deposition

Islands of constant width at half maximum of approximately 100 nm have been observed during the pulsed laser deposition of films of nominal thickness from 0.7 to 3.0 nm of the material YBa₂Cu₃O_7-δ(YBCO) on substrates of SrTiO₃. The critical island dimensions of width, height and spacing were analyzed with classical kinetic and thermodynamic theories. Analytically it was calculated that the equilibrium island width for a 29-nm-high island should be 111 nm. The analysis also predicted that islands of smaller height should be wider, and higher islands should be narrower. Islands of height from 3.5 nm to 29 nm were observed with an atomic force microscope to have a constant width at half maximum of approximately 100 nm. There are several possible differences between experiment and analysis that could explain the difference in the results: the islands formed in a non-equilibrium phase of YBCO, the island strain relaxed from the base to the top, and smaller islands may not have reached their equilibrium width. Larger islands had significant roughening at the top. Calculations predict that these islands would be unstable with respect to surface perturbations. Calculations of relaxation strain energy and surface energy showed that there was excess strain energy available for island heights above 9 nm to provide the extra surface energy that would be necessary for surface perturbations to develop. The minimum observed interisland spacing of 36 nm agreed with calculations of the average atom diffusion length (40.6 nm). Received: 2 April 2001 / Accepted: 6 September 2001 / Published online: 20 December 2001     

Critical exponents for the self-avoiding random walk in three dimensions

We compute by direct Monte Carlo simulation the main critical exponents, , ₄, andv and the effective coordination number for the self-avoiding random walk in three dimensions on a cubic lattice. We find both hyperscaling relationsdv=2– anddv– 2 ₄+=0 satisfied ind = 3.