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 [2]. 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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These developments have led to a great deal of new mathematical work. Information References 42 Citations 20 Files Plots.

A natural sequel to the first Clay monograph on Mirror Symmetry, it presents the new ideas mirrod out of the interactions of string theory and algebraic geometry in a coherent logical context. Note that the notion of an ‘A-infinity algebra’ can arise here when attempting to show equivalences between triangles of maps. Learn more about Amazon Prime.

Dirichlet Branes and Mirror Symmetry

Amazon Inspire Digital Educational Resources. We use cookies to give you the best possible experience. D-branes in Gepner models – Recknagel, A. This implies the use of the Hodge star, which depends mirdor the metric and is continuously valued. Get to Know Us. 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.


After showing how notions of branes arose in string theory, it turns to an introduction to the algebraic geometry, sheaf theory, and homological algebra needed to define and work with derived categories. There are several important ideas and concepts needed to understand the content of this book, and some of the main ones include: The notion of pi-stability reduces to theta-stability at orbifold points and mu-stability at the large volume limit, as required.

Inthe introduction of Calabi-Yau manifolds into physics as a way to compactify ten-dimensional space-time has led to exciting cross-fertilization between physics and mathematics, especially with the discovery of mirror symmetry in Quantum Fields and Strings: As foreseen by Kontsevich, these dirifhlet out to have mathematical counterparts in the derived category of coherent sheaves on an algebraic variety and the Fukaya category of a symplectic manifold.

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Dirichlet branes, homological mirror symmetry, and stability – INSPIRE-HEP

There was a problem filtering reviews right now. Dirichlet Branes and Mirror Symmetry. A natural sequel to the first Clay monograph on Mirror Symmetry, it presents the new ideas coming out of the interactions of string theory and btanes geometry in a coherent logical context.

On counting special Lagrangian homology three spheres – Joyce, Dominic Contemp. Einstein type metrics and stability on vector bundles – Leung, Naichung Conan J.


If you are a seller for this product, would you like to suggest updates through seller support? This motivates symmerty “twisting” of the NS 3-form field strength, namely the use of twisted K-theory. Amazon Renewed Refurbished products with a warranty. Top Reviews Most recent Top Reviews. Another way of viewing this is examine the generic category of pi-semistable objects with a fixed grading phi.

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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. Massless black holes and conifolds in string theory – Strominger, Andrew Nucl.

Mathematics > Algebraic Geometry

Dirichlet Branes and Mirror Symmetry. For a complex in an Abelian category, there is a notion of kernel and cokernel, which may not exist in a general category. This is different from the situation in K-theory, where a brane-antibrane pair cancels if all open strings to them cancel out of the Q-homology, i.

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.