132,391 research outputs found
On the Fukaya Categories of Higher Genus Surfaces
We construct the Fukaya category of a closed surface equipped with an area
form using only elementary (essentially combinatorial) methods. We also compute
the Grothendieck group of its derived category.Comment: 40 pages, 17 figures. Final Versio
A beginner's introduction to Fukaya categories
The goal of these notes is to give a short introduction to Fukaya categories
and some of their applications. The first half of the text is devoted to a
brief review of Lagrangian Floer (co)homology and product structures. Then we
introduce the Fukaya category (informally and without a lot of the necessary
technical detail), and briefly discuss algebraic concepts such as exact
triangles and generators. Finally, we mention wrapped Fukaya categories and
outline a few applications to symplectic topology, mirror symmetry and
low-dimensional topology. This text is based on a series of lectures given at a
Summer School on Contact and Symplectic Topology at Universit\'e de Nantes in
June 2011.Comment: 42 pages, 13 figure
Yukawa couplings in intersecting D-brane models
We compute the Yukawa couplings among chiral fields in toroidal Type II
compactifications with wrapping D6-branes intersecting at angles. Those models
can yield realistic standard model spectrum living at the intersections. The
Yukawa couplings depend both on the Kahler and open string moduli but not on
the complex structure. They arise from worldsheet instanton corrections and are
found to be given by products of complex Jacobi theta functions with
characteristics. The Yukawa couplings for a particular intersecting brane
configuration yielding the chiral spectrum of the MSSM are computed as an
example. We also show how our methods can be extended to compute Yukawa
couplings on certain classes of elliptically fibered CY manifolds which are
mirror to complex cones over del Pezzo surfaces. We find that the Yukawa
couplings in intersecting D6-brane models have a mathematical interpretation in
the context of homological mirror symmetry. In particular, the computation of
such Yukawa couplings is related to the construction of Fukaya's category in a
generic symplectic manifold.Comment: 47 pages, using JHEP3.cls, 11 figures. Typos and other minor
corrections. References adde
Magnetic Monopoles, Center Vortices, Confinement and Topology of Gauge Fields
The vortex picture of confinement is studied. The deconfinement phase
transition is explained as a transition from a phase in which vortices
percolate to a phase of small vortices. Lattice results are presented in
support of this scenario. Furthermore the topological properties of magnetic
monopoles and center vortices arising, respectively, in Abelian and center
gauges are studied in continuum Yang-Mills-theory. For this purpose the
continuum analog of the maximum center gauge is constructed.Comment: talk given by H. Reinhardt on the Int. Workshop ``Hadrons 1999'',
Coimbra, 10.-15. Sept. 199
Locked and Unlocked Chains of Planar Shapes
We extend linkage unfolding results from the well-studied case of polygonal
linkages to the more general case of linkages of polygons. More precisely, we
consider chains of nonoverlapping rigid planar shapes (Jordan regions) that are
hinged together sequentially at rotatable joints. Our goal is to characterize
the families of planar shapes that admit locked chains, where some
configurations cannot be reached by continuous reconfiguration without
self-intersection, and which families of planar shapes guarantee universal
foldability, where every chain is guaranteed to have a connected configuration
space. Previously, only obtuse triangles were known to admit locked shapes, and
only line segments were known to guarantee universal foldability. We show that
a surprisingly general family of planar shapes, called slender adornments,
guarantees universal foldability: roughly, the distance from each edge along
the path along the boundary of the slender adornment to each hinge should be
monotone. In contrast, we show that isosceles triangles with any desired apex
angle less than 90 degrees admit locked chains, which is precisely the
threshold beyond which the inward-normal property no longer holds.Comment: 23 pages, 25 figures, Latex; full journal version with all proof
details. (Fixed crash-induced bugs in the abstract.
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