4,162 research outputs found
Mirror Maps and Instanton Sums for Complete Intersections in Weighted Projective Space
We consider a class of Calabi-Yau compactifications which are constructed as
a complete intersection in weighted projective space. For manifolds with one
K\"ahler modulus we construct the mirror manifolds and calculate the instanton
sum.Comment: 10 page
Lectures on Mirror Symmetry
We give an introduction to mirror symmetry of strings on Calabi-Yau manifolds
with an emphasis on its applications e.g. for the computation of Yukawa
couplings. We introduce all necessary concepts and tools such as the basics of
toric geometry, resolution of singularities, construction of mirror pairs,
Picard-Fuchs equations, etc. and illustrate all of this on a non-trivial
example. Extended version of a lecture given at the Third Baltic Student
Seminar, Helsinki September 1993Comment: LMU-TPW-94-02, 45 pages, harvma
Stable and unstable attractors in Boolean networks
Boolean networks at the critical point have been a matter of debate for many
years as, e.g., scaling of number of attractor with system size. Recently it
was found that this number scales superpolynomially with system size, contrary
to a common earlier expectation of sublinear scaling. We here point to the fact
that these results are obtained using deterministic parallel update, where a
large fraction of attractors in fact are an artifact of the updating scheme.
This limits the significance of these results for biological systems where
noise is omnipresent. We here take a fresh look at attractors in Boolean
networks with the original motivation of simplified models for biological
systems in mind. We test stability of attractors w.r.t. infinitesimal
deviations from synchronous update and find that most attractors found under
parallel update are artifacts arising from the synchronous clocking mode. The
remaining fraction of attractors are stable against fluctuating response
delays. For this subset of stable attractors we observe sublinear scaling of
the number of attractors with system size.Comment: extended version, additional figur
Nonperturbative Effective Actions of N=2 Supersymmetric Gauge Theories
We elaborate on our previous work on N=2 supersymmetric Yang-Mills theory. In
particular, we show how to explicitly determine the low energy quantum
effective action for from the underlying hyperelliptic Riemann
surface, and calculate the leading instanton corrections. This is done by
solving Picard-Fuchs equations and asymptotically evaluating period integrals.
We find that the dynamics of the theory is governed by an Appell system
of type , and compute the exact quantum gauge coupling explicitly in terms
of Appell functions.Comment: 57p, harvmac with hyperlinks, 9 uuencoded ps figure
On the Monodromies of N=2 Supersymmetric Yang-Mills Theory
We review the generalization of the work of Seiberg and Witten on N=2
supersymmetric SU(2) Yang-Mills theory to SU(n) gauge groups. The quantum
moduli spaces of the effective low energy theory parametrize a special family
of hyperelliptic genus n-1 Riemann surfaces. We discuss the massless spectrum
and the monodromies.Comment: 15p, harvmac/lanlmac with hyperlinks, 4 uuencoded compressed
postscript figures appende
Mirror Symmetry, Mirror Map and Applications to Complete Intersection Calabi-Yau Spaces
We extend the discussion of mirror symmetry, Picard-Fuchs equations,
instanton-corrected Yukawa couplings, and the topological one-loop partition
function to the case of complete intersections with higher-dimensional moduli
spaces. We will develop a new method of obtaining the instanton-corrected
Yukawa couplings through a close study of the solutions of the Picard-Fuchs
equations. This leads to closed formulas for the prepotential for the K\"ahler
moduli fields induced from the ambient space for all complete intersections in
non singular weighted projective spaces. As examples we treat part of the
moduli space of the phenomenologically interesting three-generation models that
are found in this class. We also apply our method to solve the simplest model
in which a topology change was observed and discuss examples of complete
intersections in singular ambient spaces.Comment: 50 page
A Note on ODEs from Mirror Symmetry
We give close formulas for the counting functions of rational curves on
complete intersection Calabi-Yau manifolds in terms of special solutions of
generalized hypergeometric differential systems. For the one modulus cases we
derive a differential equation for the Mirror map, which can be viewed as a
generalization of the Schwarzian equation. We also derive a nonlinear seventh
order differential equation which directly governs the instanton corrected
Yukawa coupling.Comment: 24 pages using harvma
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