12,317 research outputs found
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
Non-symplectic automorphisms of odd prime order on manifolds of K3 [n] -type
We contribute to the classification of non-symplectic automorphisms of odd prime order on irreducible holomorphic symplectic manifolds which are deformations of Hilbert schemes of any number n of points on K3 surfaces, extending results already known for n = 2. In particular, we study the properties of the invariant lattice of the automorphism (and its orthogonal complement) inside the second cohomology lattice of the manifold. We also explain how to construct automorphisms with fixed action on cohomology: in the cases n = 3, 4 the examples provided realize all admissible actions in our classification. For n = 4, we present a construction of non-symplectic automorphisms on the Lehn\u2013Lehn\u2013Sorger\u2013van Straten eightfold, which come from automorphisms of the underlying cubic fourfold
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