262 research outputs found
The Bismut-Elworthy-Li type formulae for stochastic differential equations with jumps
Consider jump-type stochastic differential equations with the drift,
diffusion and jump terms. Logarithmic derivatives of densities for the solution
process are studied, and the Bismut-Elworthy-Li type formulae can be obtained
under the uniformly elliptic condition on the coefficients of the diffusion and
jump terms. Our approach is based upon the Kolmogorov backward equation by
making full use of the Markovian property of the process.Comment: 29 pages, to appear in Journal of Theoretical Probabilit
Pathways of glycogen synthesis from glucose during the glycogenic response to insulin in cultured foetal hepatocytes
A characterization of Dirac morphisms
Relating the Dirac operators on the total space and on the base manifold of a
horizontally conformal submersion, we characterize Dirac morphisms, i.e. maps
which pull back (local) harmonic spinor fields onto (local) harmonic spinor
fields.Comment: 18 pages; restricted to the even-dimensional cas
The Hitchin functionals and the topological B-model at one loop
The quantization in quadratic order of the Hitchin functional, which defines
by critical points a Calabi-Yau structure on a six-dimensional manifold, is
performed. The conjectured relation between the topological B-model and the
Hitchin functional is studied at one loop. It is found that the genus one free
energy of the topological B-model disagrees with the one-loop free energy of
the minimal Hitchin functional. However, the topological B-model does agree at
one-loop order with the extended Hitchin functional, which also defines by
critical points a generalized Calabi-Yau structure. The dependence of the
one-loop result on a background metric is studied, and a gravitational anomaly
is found for both the B-model and the extended Hitchin model. The anomaly
reduces to a volume-dependent factor if one computes for only Ricci-flat Kahler
metrics.Comment: 33 pages, LaTe
Positivity of relative canonical bundles and applications
Given a family of canonically polarized manifolds, the
unique K\"ahler-Einstein metrics on the fibers induce a hermitian metric on the
relative canonical bundle . We use a global elliptic
equation to show that this metric is strictly positive on , unless
the family is infinitesimally trivial.
For degenerating families we show that the curvature form on the total space
can be extended as a (semi-)positive closed current. By fiber integration it
follows that the generalized Weil-Petersson form on the base possesses an
extension as a positive current. We prove an extension theorem for hermitian
line bundles, whose curvature forms have this property. This theorem can be
applied to a determinant line bundle associated to the relative canonical
bundle on the total space. As an application the quasi-projectivity of the
moduli space of canonically polarized varieties
follows.
The direct images , , carry natural hermitian metrics. We prove an
explicit formula for the curvature tensor of these direct images. We apply it
to the morphisms that are induced by the Kodaira-Spencer map and obtain a differential
geometric proof for hyperbolicity properties of .Comment: Supercedes arXiv:0808.3259v4 and arXiv:1002.4858v2. To appear in
Invent. mat
Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmuller geodesic flow
We compute the sum of the positive Lyapunov exponents of the Hodge bundle
with respect to the Teichmuller geodesic flow. The computation is based on the
analytic Riemann-Roch Theorem and uses a comparison of determinants of flat and
hyperbolic Laplacians when the underlying Riemann surface degenerates.Comment: Minor corrections. To appear in Publications mathematiques de l'IHE
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
Global obstructions to gauge-invariance in chiral gauge theory on the lattice
It is shown that certain global obstructions to gauge-invariance in chiral
gauge theory, described in the continuum by Alvarez-Gaume and Ginsparg, are
exactly reproduced on the lattice in the Overlap formulation at small non-zero
lattice spacing (i.e. close to the classical continuum limit). As a
consequence, the continuum anomaly cancellation condition is seen
to be a necessary (although not necessarily sufficient) condition for anomaly
cancellation on the lattice in the Overlap formulation.Comment: 31 pages, latex. v4: A few minor corrections, to appear in Nucl.
Phys.
Reduction and reconstruction of stochastic differential equations via symmetries
An algorithmic method to exploit a general class of infinitesimal symmetries
for reducing stochastic differential equations is presented and a natural
definition of reconstruction, inspired by the classical reconstruction by
quadratures, is proposed. As a side result the well-known solution formula for
linear one-dimensional stochastic differential equations is obtained within
this symmetry approach. The complete procedure is applied to several examples
with both theoretical and applied relevance
The Standard Model with gravity couplings
In this paper, we examine the coupling of matter fields to gravity within the
framework of the Standard Model of particle physics. The coupling is described
in terms of Weyl fermions of a definite chirality, and employs only
(anti)self-dual or left-handed spin connection fields. It is known from the
work of Ashtekar and others that such fields can furnish a complete description
of gravity without matter. We show that conditions ensuring the cancellation of
perturbative chiral gauge anomalies are not disturbed. We also explore a global
anomaly associated with the theory, and argue that its removal requires that
the number of fundamental fermions in the theory must be multiples of 16. In
addition, we investigate the behavior of the theory under discrete
transformations P, C and T; and discuss possible violations of these discrete
symmetries, including CPT, in the presence of instantons and the
Adler-Bell-Jackiw anomaly.Comment: Extended, and replaced with LaTex file. 25 Page
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