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 . This is the second of two books that provide the scientific record of the school. The first book, Strings and Geometry, edited by Michael R. 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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Dirichlet branes and mirror symmetry – INSPIRE-HEP
This has led to exciting new work, including the Strominger—Yau—Zaslow conjecture, which used the theory of branes to propose a geometric basis for mirror symmetry, the theory of stability conditions on triangulated categories, and a physical basis for the McKay correspondence.
The authors explain how Kontsevich’s conjecture is equivalent to the identification of two different categories of Dirichlet branes. These topological theories are easier to understand and do retain a little bit of the information encoded in the full SCFTs.
Dirichlet Branes and Mirror Symmetry. Deriving the matrix model arXiv: Dr Alastair Craw Deposited On: This site is running on Instiki 0. Product details Format Hardback pages Dimensions In fact one considers mirror symmetry for degenerating families for Calabi-Yau 3-folds in large volume limit which may be expressed precisely via the Gromov-Hausdorff metric.
Dirichlet Branes and Mirror Symmetry
The Clay School on Geometry and String Theory set out to bridge this gap, and this monograph builds on the expository lectures given there to provide an up-to-date discussion including subsequent developments. Clay mathematics monographs 4.
Abstract 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 theory and algebraic geometry, presenting an updated discussion that includes subsequent developments.
The authors were not satisfied to tell their story twice, from separate mathematics and physics points of view. The mirror symmetry conjecture roughly claims that every Calabi-Yau 3-fold has a mirror. The Geometrization Conjecture John Morgan. A new string revolution in the mids brought the notion of branes to the forefront.
This is called mirror symmetry. We can notify you when this item is back in stock. The narrative is organized around two principal ideas: Libraries and resellers, please contact cust-serv ams.
Surveys 59no. Home Contact Us Help Free delivery worldwide. 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. 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.
S-dualityelectric-magnetic duality. Skip to main content Accessibility information. The topological A-model can be expressed in terms of symplectic geometry of a variety and the topological B-model can be expressed in terms of the algebraic geometry of a variety.
A few of the relevant names: The narrative is organized around two principal ideas: T-dualitymirror symmetry. Visit our Beautiful Books page and find lovely books for kids, photography lovers and more. Description Research in string theory has generated a rich interaction with algebraic geometry, with exciting new work that includes the Strominger-Yau-Zaslow conjecture.
The group of distinguished mathematicians and mathematical physicists who produced this monograph worked as a team to create a unique volume. Context Duality duality abstract duality: 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 symplectic manifold.
At least in some cases this can be understood as a special case of T-duality Strominger-Yau-Zaslow They also explore the ramifications and current state of the Strominger-Yau-Zaslow conjecture. Computation via topological recursion in matrix models and all- genus?