11,659 research outputs found
Intersecting hypersurfaces, topological densities and Lovelock Gravity
Intersecting hypersurfaces in classical Lovelock gravity are studied
exploiting the description of the Lovelock Lagrangian as a sum of dimensionally
continued Euler densities. We wish to present an interesting geometrical
approach to the problem. The analysis allows us to deal most efficiently with
the division of space-time into a honeycomb network of cells produced by an
arbitrary arrangement of membranes of matter. We write the gravitational action
as bulk terms plus integrals over each lower dimensional intersection.
The spin connection is discontinuous at the shared boundaries of the cells,
which are spaces of various dimensionalities. That means that at each
intersection there are more than one spin connections.
We introduce a multi-parameter family of connections which interpolate
between the different connections at each intersection. The parameters live
naturally on a simplex. We can then write the action including all the
intersection terms in a simple way. The Lagrangian of Lovelock gravity is
generalized so as to live on the simplices as well. Each intersection term of
the action is then obtained as an integral over an appropriate simplex.
Lovelock gravity and the associated topological (Euler) density are used as
an example of a more general formulation. In this example one finds that
singular sources up to a certain co-dimensionality naturally carry matter
without introducing conical or other singularities in spacetime geometry.Comment: 24 pages, 2 figures, version 4: lengthened introduction, section on
explicit junction conditions for intersections added. Accepted in Journal of
Geometry and Physic
Colliding Interfaces in Old and New Diffuse-interface Approximations of Willmore-flow
This paper is concerned with diffuse-interface approximations of the Willmore
flow. We first present numerical results of standard diffuse-interface models
for colliding one dimensional interfaces. In such a scenario evolutions towards
interfaces with corners can occur that do not necessarily describe the adequate
sharp-interface dynamics.
We therefore propose and investigate alternative diffuse-interface
approximations that lead to a different and more regular behavior if interfaces
collide. These dynamics are derived from approximate energies that converge to
the -lower-semicontinuous envelope of the Willmore energy, which is in
general not true for the more standard Willmore approximation
Mirror Symmetry, Mirror Map and Applications to Calabi-Yau Hypersurfaces
Mirror Symmetry, Picard-Fuchs equations and instanton corrected Yukawa
couplings are discussed within the framework of toric geometry. It allows to
establish mirror symmetry of Calabi-Yau spaces for which the mirror manifold
had been unavailable in previous constructions. Mirror maps and Yukawa
couplings are explicitly given for several examples with two and three moduli.Comment: 59 pages. Some changes in the references, a few minor points have
been clarifie
Inflation and topological phase transition driven by exotic smoothness
In this paper we will discuss a model which describes the cause of inflation
by a topological transition. The guiding principle is the choice of an exotic
smoothness structure for the space-time. Here we consider a space-time with
topology . In case of an exotic ,
there is a change in the spatial topology from a 3-sphere to a homology
3-sphere which can carry a hyperbolic structure. From the physical point of
view, we will discuss the path integral for the Einstein-Hilbert action with
respect to a decomposition of the space-time. The inclusion of the boundary
terms produces fermionic contributions to the partition function. The
expectation value of an area (with respect to some surface) shows an
exponential increase, i.e. we obtain inflationary behavior. We will calculate
the amount of this increase to be a topological invariant. Then we will
describe this transition by an effective model, the Starobinski or
model which is consistent with the current measurement of the Planck satellite.
The spectral index and other observables are also calculated. Finally we obtain
a realistic cosmological constant.Comment: 21 pages, no figures, iopart styla, accepted in Advances in High
Energy Physics, special issue "Experimental Tests of Quantum Gravity and
Exotic Quantum Field Theory Effects (QGEQ)
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