Wilson surfaces and higher dimensional knot invariants

An observable for nonabelian, higher-dimensional forms is introduced, its properties are discussed and its expectation value in BF theory is described. This is shown to produce potential and genuine invariants of higher-dimensional knots.Comment: 31 pages, 9 figure

Quasars and galaxy formation

Quasars are widely believed to be powered by accretion onto supermassive black holes and there is now considerable evidence for a link between mergers, quasars and the formation of spheroids. Cattaneo, Haehnelt & Rees (1999) have demonstrated that a very simple model in which supermassive black holes form and accrete most of their mass in mergers of galaxies of comparable masses can reproduce the observed relation of black hole mass to bulge luminosity. Here we show that this simple model can account for the luminosity function of quasars and for the redshift evolution of the quasar population provided a few additional assumptions are made. We use the extended Press-Schechter formalism to simulate the formation of galaxies in hierarchical models of the formation of structures and we assume that, when two galaxies of comparable masses merge, their central black holes coalesce and a fraction of the gas in the merger remnant is accreted by the supermassive black hole over a time-scale of about 10^7 yr. We find that the decrease in the merging rate with cosmic time and the depletion in the amount of cold gas available due to the formation of stars are not sufficient to explain the strong decline in the space density of bright quasars between z=2 and z=0, since larger and larger structures form, which can potentially host brighter and brighter quasars. To explain the redshift evolution of the space density of bright quasars between z=2 and z=0 we need to assume that there is a dependence on redshift either in the fraction of available gas accreted or in the time-scale for accretion.Comment: 8 pages, 8 figures, submitted to MNRA

Dispersion relations for the time-fractional Cattaneo-Maxwell heat equation

In this paper, after a brief review of the general theory of dispersive waves in dissipative media, we present a complete discussion of the dispersion relations for both the ordinary and the time-fractional Cattaneo-Maxwell heat equations. Consequently, we provide a complete characterization of the group and phase velocities for these two cases, together with some non-trivial remarks on the nature of wave dispersion in fractional models.Comment: 18 pages, 7 figure

Integral Invariants of 3-Manifolds

This note describes an invariant of rational homology 3-spheres in terms of configuration space integrals which in some sense lies between the invariants of Axelrod and Singer and those of Kontsevich.Comment: 39 pages, AMS-LaTeX, to appear in J. Diff. Geo

Black Holes and Cosmological Constant in Bosonic String Theory: Some Remarks

(some corrections in the semiclassical study and one reference added).Comment: 17 pages; PHYZZX; IFUM 450/F

Coisotropic submanifolds in Poisson geometry and branes in the Poisson sigma model

General boundary conditions ("branes") for the Poisson sigma model are studied. They turn out to be labeled by coisotropic submanifolds of the given Poisson manifold. The role played by these boundary conditions both at the classical and at the perturbative quantum level is discussed. It turns out to be related at the classical level to the category of Poisson manifolds with dual pairs as morphisms and at the perturbative quantum level to the category of associative algebras (deforming algebras of functions on Poisson manifolds) with bimodules as morphisms. Possibly singular Poisson manifolds arising from reduction enter naturally into the picture and, in particular, the construction yields (under certain assumptions) their deformation quantization.Comment: 21 pages, 2 figures; minor corrections, references updated; final versio

A cellular topological field theory

We present a construction of cellular BF theory (in both abelian and non-abelian variants) on cobordisms equipped with cellular decompositions. Partition functions of this theory are invariant under subdivisions, satisfy a version of the quantum master equation, and satisfy Atiyah-Segal-type gluing formula with respect to composition of cobordisms

How do galaxies acquire their mass?

We introduce a toy model that describes (in a single equation) the mass in stars as a function of halo mass and redshift. Our model includes the suppression of gas accretion from gravitational shock heating and AGN jets mainly for M_halo > M_shock ~ 10^12 M_Sun and from a too hot IGM onto haloes with v_circ < 40 km/s, as well as stellar feedback that drives gas out of haloes mainly with v_circ < 120 km/s. We run our model on the merger trees of the haloes and subhaloes of a high-resolution dark matter cosmological simulation. The galaxy mass is taken as the maximum between the mass given by the model and the sum of the masses of its progenitors (reduced by tidal stripping). Designed to reproduce the present-day stellar mass function of galaxies, our model matches fairly well the evolution of the cosmic stellar density. It leads to the same z=0 relation between central galaxy stellar and halo mass as the one found by abundance matching and also as that previously measured at high mass on SDSS centrals. Our model also predicts a bimodal distribution (centrals and satellites) of stellar masses for given halo mass, in good agreement with SDSS observations. The relative importance of mergers depends much more on stellar than halo mass. Galaxies with m_stars > 10^11 M_Sun/h acquire most of their mass through mergers (mostly major and gas-poor), as expected from our model's shutdown of gas accretion at high M_halo. However, mergers are rare for m_stars < 10^11 M_Sun/h (greater than our mass resolution), a consequence of the curvature of the stellar vs. halo mass relation. So gas accretion must be the dominant growth mechanism for intermediate and low mass galaxies, e.g. dwarf ellipticals in clusters, except that gas-rich galaxy mergers account for the bulk of the growth of ellipticals with m_stars ~ 10^10.5 M_Sun/h, which we predict must be the typical mass of ULIRGs.Comment: 18 pages, 12 figures, A&A in press (major re-write and updated figures from version 1

Everything you always wanted to know about wto accession (but were afraid to ask)

In this paper, the authors explore the complex, long, and unique process of accession to the World Trade Organization, with its intertwined economic, legal, and political dimensions. Referring to country case studies and sector-specific issues, the paper organizes some of the current reflections on the topic around three main themes. First, it explores the rationale of accession to the World Trade Organization: Why would new members join the WTO? And why would incumbent members let new members in? Second, it analyzes the World Trade Organization accession process in detail: What are the main characteristics and challenges of the accession process? Has it evolved over time, and how? Third, the paper looks at the implementation of World Trade Organization accession deals: Is accession the end or the beginning of the story? What are the implications for the participating countries and the multilateral trading system?World Trade Organization,Economic Theory&Research,Trade and Services,Trade Law,Debt Markets