This has led to the formulation of a notion of stability for objects in a derived category, contact with Kontsevich’s homological mirror symmetry conjecture, and . We present a justification on the conjecture on the mirror construction of D- branes in Aganagic-Vafa . We apply the techniques employed in. PDF | This monograph builds on lectures at the Clay School on Geometry and String Theory that sought to bridge the gap between the languages of string .
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B UTTG In somewhat more detail, to classify fluxes on a compact dimensional space-time must deal with the fact that RR fluxes are self-dual.
The book first introduces the notion of Dirichlet brane in the context of topological quantum field theories, and then reviews the basics of string theory. ComiXology Thousands of Digital Comics. A natural question to ask here is if a cohomology classification is in anyway tenable since Type II strings in the classical limit is Type II supergravity wherein the RR field strengths are differential forms.
Page 1 of 1 Start over Page 1 of 1. One difficulty in understanding all aspects of this work is that it requires being able to speak two different languages, the language of string theory and the language of algebraic geometry. In this context, a binding process can be viewed as a formation, wherein two D-branes can bind together via a potentially tachyonic open string.
Dirichlet branes, homological mirror symmetry, and stability – INSPIRE-HEP
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Amazon Inspire Digital Educational Resources. The K-theory classification classifies the allowed RR field strengths as well as the charges of stable D-branes. Dirichlet Branes and Mirror Symmetry. We hope it will branez students and researchers who are familiar with the language of one of the two fields to gain acquaintance with the language of the other.
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In a derived category the morphisms do not have kernels or cokernels, and so they are ‘additive’ but not Abelian. Its overall goal is to explore the physical and mathematical aspects of Symmetrj branes. Amazon Rapids Fun stories for kids on the go. Home Contact Us Help Free delivery worldwide. Dirichlet Branes and Mirror Symmetry Share this page.
Other books in this series. See our librarian page for additional eBook ordering options. Fukaya categories may not have a triangulated structure, so there is a need to add “potentially stable” A-branes to the Fukaya category so that it becomes triangulated.
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This determines which elements in a derived category actually correspond to physical BPS D-branes. But topologically distinct RR field strengths can branex in configurations free of branes, and so the integral cohomology is too large.
A new string revolution in the mids brought the notion of branes to the forefront. Print Price 2 Label: The Geometrization Conjecture John Morgan. There was a problem filtering reviews right now.
Mathematics > Symplectic Geometry
There’s a problem loading this menu right now. Nonlinear instantons from supersymmetric p-branes – Marino, Marcos et al. This implies the need for D-branes at generic points in moduli space to have “sub” D-branes, which implies the need for a notion of “subobject” of an object in the category of D-branes.
As foreseen by Kontsevich, these turned out to have mathematical counterparts in the derived category of coherent sheaves on an algebraic variety and the Fukaya category of a miirror manifold.
Dirichlet Branes and Mirror Symmetry : Bennett Chow :
We hope it will allow students and researchers who are familiar with the language of one of the two fields to gain acquaintance with the language of the other. Add both to Cart Add both to List. In sheaf theory, a similar issue arises in that a surjection of diruchlet will not in general be surjective on local sections, i. A Bestiary Mirror Physicists. Join our email list. Clay Mathematics Monographs Volume: A distinguished triangle will not permit the decay of a stable B-brane into two other stable B-branes.
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