3,551 research outputs found
Some results on homoclinic and heteroclinic connections in planar systems
Consider a family of planar systems depending on two parameters and
having at most one limit cycle. Assume that the limit cycle disappears at some
homoclinic (or heteroclinic) connection when We present a method
that allows to obtain a sequence of explicit algebraic lower and upper bounds
for the bifurcation set The method is applied to two quadratic
families, one of them is the well-known Bogdanov-Takens system. One of the
results that we obtain for this system is the bifurcation curve for small
values of , given by . We obtain
the new three terms from purely algebraic calculations, without evaluating
Melnikov functions
Nonsupersymmetric Flux Vacua and Perturbed N=2 Systems
We geometrically engineer N=2 theories perturbed by a superpotential by
adding 3-form flux with support at infinity to local Calabi-Yau geometries in
type IIB. This allows us to apply the formalism of Ooguri, Ookouchi, and Park
[arXiv:0704.3613] to demonstrate that, by tuning the flux at infinity, we can
stabilize the dynamical complex structure moduli in a metastable,
supersymmetry-breaking configuration. Moreover, we argue that this setup can
arise naturally as a limit of a larger Calabi-Yau which separates into two
weakly interacting regions; the flux in one region leaks into the other, where
it appears to be supported at infinity and induces the desired superpotential.
In our endeavor to confirm this picture in cases with many 3-cycles, we also
compute the CIV-DV prepotential for arbitrary number of cuts up to fifth order
in the glueball fields.Comment: 70 pages (47 pages + 4 appendices), 10 figure
Exceptional SW Geometry from ALE Fibrations
We show that the genus 34 Seiberg-Witten curve underlying Yang-Mills
theory with gauge group yields physically equivalent results to the
manifold obtained by fibration of the ALE singularity. This reconciles a
puzzle raised by string duality
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