DIRICHLET BRANES AND MIRROR SYMMETRY PDF

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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Its overall goal is to explore the physical and mathematical aspects of Dirichlet branes. Context Duality duality abstract duality: Request a correction Enlighten Editors: Publication Month and Year: The group of distinguished mathematicians and mathematical physicists who produced this monograph worked as a team to create a unique volume.

Mirror symmetry is related to the T-duality on each fiber of an associated Lagrangian fibration Strominger-Yau-Zaslow The relation to T-duality was established in.

Dirichlet branes and mirror symmetry – INSPIRE-HEP

In terms of these the statement of mirror symmetry says that passing to mirror CYs exchanges the A-model with the B B -model and conversely:. Instead, theirs is a unified presentation offered in a way that both mathematicians and physicists can follow, without having all of the foundations of both subjects at their immediate disposal.

By using our website you agree to our use of cookies. Deriving the matrix model arXiv: We use cookies to give you the best possible experience. Clay Mathematics Monographs Volume: Print Price 1 Label: The appropriate definition of an appropriate version of the Fukaya category of a symplectic manifold is difficult to achieve in desired generality. Visit our Beautiful Books page and find lovely books for kids, photography lovers and more.

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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. Surveys 59no. Graduate students and research mathematicians interested in mathematical aspects of quantum field theory, in particular string theory and mirror symmetry. The authors explain how Kontsevich’s conjecture is equivalent to the identification of two different categories of Dirichlet branes.

The mirror symmetry conjecture roughly claims that every Calabi-Yau 3-fold has a mirror. The physical existence conditions for branes are then discussed and compared in the context of mirror symmetry, culminating in Bridgeland’s definition of stability structures, and its applications to the McKay correspondence and quantum geometry.

We’re featuring millions of their reader ratings on our book pages to help you find your new favourite book. The book continues with detailed treatments of the Strominger—Yau—Zaslow conjecture, Calabi—Yau metrics and homological mirror symmetry, and discusses more recent physical developments.

Dirichlet Branes and Mirror Symmetry

Dirichlet Branes and Mirror Symmetry. OrlovMirror symmetry for Del Pezzo surfaces: Discussion in the context of derived Morita equivalence includes. They relate the ideas to active areas of research that include the McKay correspondence, topological diricylet field theory, and stability structures.

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Mathematics > Algebraic Geometry

They also explore the ramifications and current state of the Strominger-Yau-Zaslow conjecture. The Geometrization Conjecture John Morgan.

Print Price 2 Label: Smith, Homological mirror symmetry for the four-torusDuke Math. Its overall goal is to explore the physical and mathematical aspects of Dirichlet branes.

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Orlov, Mirror symmetry for abelian varietiesJ. Cumrun VafaShing-Tung Yau eds. At least in some cases this can be understood as a special case of T-duality Strominger-Yau-Zaslow 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.

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. They relate the ideas to active diichlet of research that include the McKay correspondence, topological quantum field theory, and stability structures.

This is called mirror symmetry.

D1-braneD3-braneD5-brane. 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 diridhlet conditions on triangulated categories, and a physical basis for the McKay correspondence.

RR-fielddifferential K-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. Contact us The University of Glasgow is a registered Scottish charity: Other books in this series. Clay mathematics monographs 4. The Best Books of Book ratings by Goodreads.