Brane Cosmology From Heterotic String Theory

We consider brane cosmologies within the context of five-dimensional effective actions with higher curvature corrections. The actions are compatible with bulk string amplitude calculations from heterotic string theory. We find wrapped solutions that satisfy the field equations in an approximate but acceptable manner given their complexity, where the internal, four-dimensional, scale factor is naturally inflating, having an exponential De-Sitter form. The temporal dependence of the metric components is nontrivial so that this metric cannot be factored as in a conformally flat case. The effective Planck mass is finite and the brane solutions can localize four-dimensional gravity while the four-dimensional gravitational constant varies with time. The Hubble constant can be freely specified through the initial value of the scalar field, to conform with recent data.     

Nonabelions in the fractional quantum hall effect

Applications of conformal field theory to the theory of fractional quantum Hall systems are discussed. In particular, Laughlin's wave function and its cousins are interpreted as conformal blocks in certain rational conformal field theories. Using this point of view a hamiltonian is constructed for electrons for which the ground state is known exactly and whose quasihole excitations have nonabelian statistics; we term these objects “nonabelions”. It is argued that universality classes of fractional quantum Hall systems can be characterized by the quantum numbers and statistics of their excitations. The relation between the order parameter in the fractional quantum Hall effect and the chiral algebra in rational conformal field theory is stressed, and new order parameters for several states are given.     

String cosmology

In this review, we discuss various cosmological issues related to our Universe from a string theoretic perspective. We analyse the pre-big bang cosmological scenario which appears naturally in this context due to the existence of scale factor duality symmetry in string theory. We then discuss some of the attractive and problematic features of this scenario. Finally, we introduce a method which is powerful enough to search for cosmological solutions in various low energy limits of string theories.     

Quantum Neural Nets

The capacity of classical neurocomputers islimited by the number of classical degrees of freedom,which is roughly proportional to the size of thecomputer. By contrast, a hypothetical quantumneurocomputer can implement an exponentially larger number ofthe degrees of freedom within the same size. In thispaper an attempt is made to reconcile the linearreversible structure of quantum evolution with nonlinear irreversible dynamics for neuralnets.     

String Theory

After reviewing the original motivation for the formulation of string theory and what we learned from it, I discuss some of the implications of the holographic principle and of string dualities for the question of the building blocks of nature.     

String Without Strings

Scale invariance provides a principled reason for the physical importance of Hilbert space, the Virasoro algebra, the string mode expansion, canonical commutators and Schrödinger evolution of states, independent of the assumptions of string theory and quantum theory. The usual properties of dimensionful fields imply an infinite, projective tower of conformal weights associated with the tangent space to scale-invariant spacetimes. Convergence and measurability on this tangent tower are guaranteed using a scale-invariant norm, restricted to conformally self-dual vectors. Maps on the resulting Hilbert space are correspondingly restricted to semi-definite conformal weight. We find the maximally- and minimally-commuting, complete Lie algebras of definite-weight operators. The projective symmetry of the tower gives these algebras central charges, giving the canonical commutator and quantum Virasoro algebras, respectively. Using a continuous, m-parameter representation for rank-m tower tensors, we show that the parallel transport equation for the momentum-vector of a particle is the Schrödinger equation, while the associated definite-weight operators obey canonical commutation relations. Generalizing to the set of integral curves of general timelike, self-dual vector-valued weight maps gives a lifting such that the action of the curves parallel transports arbitrary tower vectors. We prove that the full set of Schrödinger-lifted integral curves of a general self-dual map gives an immersion of its 2-dim parameter space into spacetime, inducing a Lorentzian metric on the parameter space. This immersion is shown to satisfy the full variational equations of open string.     

Integrable Models: from Dynamical Solutions to String Theory

We review the status of integrable models from the point of view of their dynamics and integrability conditions. A few integrable models are discussed in detail. We comment on the use it is made of them in string theory. We also discuss the SO(6) symmetric Hamiltonian with SO(6) boundary. This work is especially prepared for the 70th anniversaries of André Swieca (in memoriam) and Roland K?berle.     

Nonsingular Inhomogeneous String Cosmology

Inhomogeneous cosmological models are consideredfor the low energy string cosmological effective action(tree level) in the absence of dilaton potential. Anon-singular and non-diagonal analytic solution isfound.     

String theory and gravity

It is pointed out that string-loop effects may generate matter couplings for the dilaton allowing this scalar partner of the tensorial graviton to stay massless while contributing to macroscopic gravity in a way naturally compatible with existing experimental data. Under a certain assumption of universality of the dilaton coupling functions, the cosmological evolution drives the dilaton towards values where it decouples from matter. At the present cosmological epoch, the coupling to matter of the dilaton should be very small, but non zero. This provides a new motivation for improving the experimental tests of Einstein's Equivalence Principle.This essay received the first award from the Gravity Research Foundation, 1994-Ed.     

String dynamics in QCD

Recent works of the authors on string interpretation of the Wilson loop operators in QCD are reviewed in a self-contained fashion. Although most of the results have already appeared in print, some new materials is presented on renormalization of the Wilson loop operator and on the use of light-cone expansion to derive a linear string-like equation in light-cone formalism.     

String theory and cosmology

We discuss the main cosmological implications of considering string-loop effects and a potential for the dilaton in the lowest order string effective action. Our framework is based on the effective model arising from regarding homogeneous and isotropic dilaton, metric and Yang-Mills field configurations. The issues of inflation, entropy crisis and the Polonyi problem as well as the problem of the cosmological constant are discussed.     

Integrable Discrete Nets in Grassmannians

We consider discrete nets in Grassmannians , which generalize Q-nets (maps with planar elementary quadrilaterals) and Darboux nets (-valued maps defined on the edges of such that quadruples of points corresponding to elementary squares are all collinear). We give a geometric proof of integrability (multidimensional consistency) of these novel nets, and show that they are analytically described by the noncommutative discrete Darboux system.