Supersymmetric 4D Orientifolds of Type IIA with D6-branes at Angles

We study a certain class of four-dimensional N=1 supersymmetric orientifolds for which the world-sheet parity transformation is combined with a complex conjugation in the compact directions. We investigate in detail the orientifolds of the Z_3, Z_4, Z_6 and Z_6' toroidal orbifolds finding solutions to the tadpole cancellation conditions for all models. Generically, all the massless spectra turn out to be non-chiral.Comment: 28 pages, LaTeX, 6 figures; v2: slight modification of closed string spectr

Three (Marginal?) Questions Regarding Convergence

This paper focuses on three (marginal?) questions surrounding the analysis of economic convergence and uses Spanish provinces as a means of illustration. The three questions in hand are the following: (i) given that the geographical units of analysis are usually quite different in economic size, is the weighting of economic units relevant in convergence analysis? (ii) the average per capita income of a given region, or country, is the first moment in the distribution of income, but what about the second moment, inequality? Have we converged in inequality? and (iii) an aggregate welfare index must take into account, at least, the evolution of the first two moments of the distribution of income, and so does the adjustment for inequality make important differences in the evolution of average per capita income? The answer to the first two questions is yes, but to the third it is clearly no.Convergence, income distribution, inequality indices and regional analysis

Quantum Gravity via Causal Dynamical Triangulations

"Causal Dynamical Triangulations" (CDT) represent a lattice regularization of the sum over spacetime histories, providing us with a non-perturbative formulation of quantum gravity. The ultraviolet fixed points of the lattice theory can be used to define a continuum quantum field theory, potentially making contact with quantum gravity defined via asymptotic safety. We describe the formalism of CDT, its phase diagram, and the quantum geometries emerging from it. We also argue that the formalism should be able to describe a more general class of quantum-gravitational models of Horava-Lifshitz type.Comment: To appear in "Handbook of Spacetime", Springer Verlag. 31 page

Noncommutative Compactifications of Type I Strings on Tori with Magnetic Background Flux

We construct six- and four-dimensional toroidal compactifications of the Type I string with magnetic flux on the D-branes. The open strings in this background probe a noncommutative internal geometry. Phenomenologically appealing features such as chiral fermions and supersymmetry breaking in the gauge sector are naturally realized by these vacua. We investigate the spectra of such noncommutative string compactifications and in a bottom-up approach discuss the possibility to obtain the standard or some GUT like model.Comment: TeX harvmac, 25 pages, 5 figure