18 research outputs found
The anomaly line bundle of the self-dual field theory
In this work, we determine explicitly the anomaly line bundle of the abelian
self-dual field theory over the space of metrics modulo diffeomorphisms,
including its torsion part. Inspired by the work of Belov and Moore, we propose
a non-covariant action principle for a pair of Euclidean self-dual fields on a
generic oriented Riemannian manifold. The corresponding path integral allows to
study the global properties of the partition function over the space of metrics
modulo diffeomorphisms. We show that the anomaly bundle for a pair of self-dual
fields differs from the determinant bundle of the Dirac operator coupled to
chiral spinors by a flat bundle that is not trivial if the underlying manifold
has middle-degree cohomology, and whose holonomies are determined explicitly.
We briefly sketch the relevance of this result for the computation of the
global gravitational anomaly of the self-dual field theory, that will appear in
another paper.Comment: 41 pages. v2: A few typos corrected. Version accepted for publication
in CM
On the geometrization of matter by exotic smoothness
In this paper we discuss the question how matter may emerge from space. For
that purpose we consider the smoothness structure of spacetime as underlying
structure for a geometrical model of matter. For a large class of compact
4-manifolds, the elliptic surfaces, one is able to apply the knot surgery of
Fintushel and Stern to change the smoothness structure. The influence of this
surgery to the Einstein-Hilbert action is discussed. Using the Weierstrass
representation, we are able to show that the knotted torus used in knot surgery
is represented by a spinor fulfilling the Dirac equation and leading to a
mass-less Dirac term in the Einstein-Hilbert action. For sufficient complicated
links and knots, there are "connecting tubes" (graph manifolds, torus bundles)
which introduce an action term of a gauge field. Both terms are genuinely
geometrical and characterized by the mean curvature of the components. We also
discuss the gauge group of the theory to be U(1)xSU(2)xSU(3).Comment: 30 pages, 3 figures, svjour style, complete reworking now using
Fintushel-Stern knot surgery of elliptic surfaces, discussion of Lorentz
metric and global hyperbolicity for exotic 4-manifolds added, final version
for publication in Gen. Rel. Grav, small typos errors fixe
Cosmological Creation of D-branes and anti-D-branes
We argue that the early universe may be described by an initial state of
space-filling branes and anti-branes. At high temperature this system is
stable. At low temperature tachyons appear and lead to a phase transition,
dynamics, and the creation of D-branes. These branes are cosmologically
produced in a generic fashion by the Kibble mechanism. From an entropic point
of view, the formation of lower dimensional branes is preferred and
brane-worlds are exponentially more likely to form than higher dimensional
branes. Virtually any brane configuration can be created from such phase
transitions by adjusting the tachyon profile. A lower bound on the number
defects produced is: one D-brane per Hubble volume.Comment: 30 pages, 5 eps figures; v2 more references added; v3 section 4
slightly improve
Primary decomposition and the fractal nature of knot concordance
For each sequence of polynomials, P=(p_1(t),p_2(t),...), we define a
characteristic series of groups, called the derived series localized at P.
Given a knot K in S^3, such a sequence of polynomials arises naturally as the
orders of certain submodules of the sequence of higher-order Alexander modules
of K. These group series yield new filtrations of the knot concordance group
that refine the (n)-solvable filtration of Cochran-Orr-Teichner. We show that
the quotients of successive terms of these refined filtrations have infinite
rank. These results also suggest higher-order analogues of the p(t)-primary
decomposition of the algebraic concordance group. We use these techniques to
give evidence that the set of smooth concordance classes of knots is a fractal
set. We also show that no Cochran-Orr-Teichner knot is concordant to any
Cochran-Harvey-Leidy knot.Comment: 60 pages, added 4 pages to introduction, minor corrections otherwise;
Math. Annalen 201