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
The spectral curve and mirror geometry arXiv: Request a symmwtry Enlighten Editors: Seiberg dualityAGT conjecture. 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.
Goodreads is the world’s largest site for readers with over 50 million reviews. The physical existence conditions for branes are then discussed and compared in the context of mirror symmefry, culminating in Bridgeland’s definition of stability structures, and its applications to the McKay correspondence and quantum geometry.
Zaslow, Mirror symmetry is T T -duality as pages —. Skip to main content Accessibility mirrorr. Looking for beautiful books? The narrative is organized around two principal ideas: 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:.
Dirichlet Branes and Mirror Symmetry.
This categorical formulation was introduced by Maxim Kontsevich in under the name homological mirror symmetry. 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 digichlet basis for the McKay correspondence.
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. Research in string theory over the last several decades has yielded a rich interaction with algebraic geometry. They relate the ideas to active areas of research that include the McKay correspondence, topological dirichllet field theory, symmetrry stability structures. 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.
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.
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mirror symmetry in nLab
At least in some cases this can be understood as a special case of T-duality Strominger-Yau-Zaslow D0-braneD2-braneD4-brane.
Langlands dualitygeometric Langlands dualityquantum geometric Langlands duality. 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.
Zaslow, Categorical mirror symmetry: Orlov, Mirror symmetry for abelian dirichpetJ. They relate the ideas to active areas of research that include the McKay correspondence, topological quantum field theory, and stability structures.
This book is suitable for graduate students and researchers with either a physics or mathematics background, who are interested in the interface between string theory and algebraic geometry. 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.
Algebraic Geometry, to appear, arXiv: The authors were not satisfied to tell their story twice, from separate mathematics and physics points of view.
Ballard, Meet homological mirror symmetry arxiv: Dirichlet Branes and Mirror Symmetry. Graduate students and research mathematicians interested in mathematical aspects bbranes quantum field theory, in particular string theory and mirror symmetry.