431 research outputs found
A Compact Codimension Two Braneworld with Precisely One Brane
Building on earlier work on football shaped extra dimensions, we construct a
compact codimension two braneworld with precisely one brane. The two extra
dimensions topologically represent a 2-torus which is stabilized by a bulk
cosmological constant and magnetic flux. The torus has positive constant
curvature almost everywhere, except for a single conical singularity at the
location of the brane. In contradistinction to the football shaped case, there
is no fine-tuning required for the brane tension. We also present some
plausibility arguments why the model should not suffer from serious stability
issues.Comment: 13 pages, 2 figures; references added, typos fixes; essentially the
version published in PR
Sobolev Inequalities for Differential Forms and -cohomology
We study the relation between Sobolev inequalities for differential forms on
a Riemannian manifold and the -cohomology of that manifold.
The -cohomology of is defined to be the quotient of the space
of closed differential forms in modulo the exact forms which are
exterior differentials of forms in .Comment: This paper has appeared in the Journal of Geometric Analysis, (only
minor changes have been made since verion 1
The H\"older-Poincar\'e Duality for -cohomology
We prove the following version of Poincare duality for reduced
-cohomology: For any , the -cohomology of a
Riemannian manifold is in duality with the interior 1/p+1/p'=11/q+1/q'=1$.Comment: 21 page
The modular geometry of Random Regge Triangulations
We show that the introduction of triangulations with variable connectivity
and fluctuating egde-lengths (Random Regge Triangulations) allows for a
relatively simple and direct analyisis of the modular properties of 2
dimensional simplicial quantum gravity. In particular, we discuss in detail an
explicit bijection between the space of possible random Regge triangulations
(of given genus g and with N vertices) and a suitable decorated version of the
(compactified) moduli space of genus g Riemann surfaces with N punctures. Such
an analysis allows us to associate a Weil-Petersson metric with the set of
random Regge triangulations and prove that the corresponding volume provides
the dynamical triangulation partition function for pure gravity.Comment: 36 pages corrected typos, enhanced introductio
Bernhard Riemann 1861 revisited: existence of flat coordinates for an arbitrary bilinear form
We generalize the celebrated results of Bernhard Riemann and Gaston Darboux:
we give necessary and sufficient conditions for a bilinear form to be flat.
More precisely, we give explicit necessary and sufficient conditions for a
tensor field of type (0,2) which is not necessary symmetric or skew-symmetric,
and is possibly degenerate, to have constant entries in a local coordinate
system.Comment: 27 page
Footballs, Conical Singularities and the Liouville Equation
We generalize the football shaped extra dimensions scenario to an arbitrary
number of branes. The problem is related to the solution of the Liouville
equation with singularities and explicit solutions are presented for the case
of three branes. The tensions of the branes do not need to be tuned with each
other but only satisfy mild global constraints.Comment: 15 pages, Refs. added, minor changes. Typo in eq. 4.3 corrected.
Version to be published in PR
Wetting to Non-wetting Transition in Sodium-Coated C_60
Based on ab initi and density-functional theory calculations, an empirical
potential is proposed to model the interaction between a fullerene molecule and
many sodium atoms. This model predicts homogeneous coverage of C_60 below 8 Na
atoms, and a progressive droplet formation above this size. The effects of
ionization, temperature, and external electric field indicate that the various,
and apparently contradictory, experimental results can indeed be put into
agreement.Comment: 4 pages, 4 postscript figure
Triangulations and volume form on moduli spaces of flat surfaces
In this paper, we are interested in flat metric structures with conical
singularities on surfaces which are obtained by deforming translation surface
structures. The moduli space of such flat metric structures can be viewed as
some deformation of the moduli space of translation surfaces. Using geodesic
triangulations, we define a volume form on this moduli space, and show that, in
the well-known cases, this volume form agrees with usual ones, up to a
multiplicative constant.Comment: 42 page
Higher dimensional abelian Chern-Simons theories and their link invariants
The role played by Deligne-Beilinson cohomology in establishing the relation
between Chern-Simons theory and link invariants in dimensions higher than three
is investigated. Deligne-Beilinson cohomology classes provide a natural abelian
Chern-Simons action, non trivial only in dimensions , whose parameter
is quantized. The generalized Wilson -loops are observables of the
theory and their charges are quantized. The Chern-Simons action is then used to
compute invariants for links of -loops, first on closed
-manifolds through a novel geometric computation, then on
through an unconventional field theoretic computation.Comment: 40 page
- …