16 research outputs found
Mellin-Barnes integrals as Fourier-Mukai transforms
We study the generalized hypergeometric system introduced by Gelfand,
Kapranov and Zelevinsky and its relationship with the toric Deligne-Mumford
(DM) stacks recently studied by Borisov, Chen and Smith. We construct series
solutions with values in a combinatorial version of the Chen-Ruan (orbifold)
cohomology and in the -theory of the associated DM stacks. In the spirit of
the homological mirror symmetry conjecture of Kontsevich, we show that the
-theory action of the Fourier-Mukai functors associated to basic toric
birational maps of DM stacks are mirrored by analytic continuation
transformations of Mellin-Barnes type.Comment: 55 pages, LaTe
Massless D-Branes on Calabi-Yau Threefolds and Monodromy
We analyze the link between the occurrence of massless B-type D-branes for
specific values of moduli and monodromy around such points in the moduli space.
This allows us to propose a classification of all massless B-type D-branes at
any point in the moduli space of Calabi-Yau's. This classification then
justifies a previous conjecture due to Horja for the general form of monodromy.
Our analysis is based on using monodromies around points in moduli space where
a single D-brane becomes massless to generate monodromies around points where
an infinite number become massless. We discuss the various possibilities within
the classification.Comment: 29 pages, LaTeX2e, 3 figures, author order fixe
A Point's Point of View of Stringy Geometry
The notion of a "point" is essential to describe the topology of spacetime.
Despite this, a point probably does not play a particularly distinguished role
in any intrinsic formulation of string theory. We discuss one way to try to
determine the notion of a point from a worldsheet point of view. The derived
category description of D-branes is the key tool. The case of a flop is
analyzed and Pi-stability in this context is tied in to some ideas of
Bridgeland. Monodromy associated to the flop is also computed via Pi-stability
and shown to be consistent with previous conjectures.Comment: 15 pages, 3 figures, ref adde
Solitons in Seiberg-Witten Theory and D-branes in the Derived Category
We analyze the "geometric engineering" limit of a type II string on a
suitable Calabi-Yau threefold to obtain an N=2 pure SU(2) gauge theory. The
derived category picture together with Pi-stability of B-branes beautifully
reproduces the known spectrum of BPS solitons in this case in a very explicit
way. Much of the analysis is particularly easy since it can be reduced to
questions about the derived category of CP1.Comment: 20 pages, LaTex2
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Discriminants and toric K-theory
We discuss a categorical approach to the theory of discriminants in thecombinatorial language introduced by Gelfand, Kapranov and Zelevinsky. Ourpoint of view is inspired by homological mirror symmetry and provides--theoretic evidence for a conjecture presented by Paul Aspinwall in aconference talk in Banff in March 2016 and later in a joint paper with Plesserand Wang