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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Print Price 1 Label: 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. Explore the Home Gift Guide. The notion of a t-structure is used to detect different Abelian categories inside a derived category. K theory and Ramond-Ramond charge – Minasian, Ruben et al.

### Dirichlet branes and mirror symmetry – INSPIRE-HEP

Research in string theory over the last several decades has yielded a rich interaction with algebraic geometry. In somewhat more detail, to classify fluxes on a compact dimensional mirroe must deal with the fact that RR fluxes are self-dual. Einstein type metrics and stability on vector bundles – Leung, Naichung Conan J.

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. There’s a problem loading branea menu right now. Discover Prime Book Box for Kids.

## Dirichlet Branes and Mirror Symmetry

Note that the notion of an ‘A-infinity algebra’ can arise here when attempting to show equivalences between triangles of maps. The mapping cone construction in a derived category gives a triangulated structure on the category, which is very important in the notion of D-brane stability, and defines a potential bound state of two D-branes.

Book ratings by Goodreads. 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. This review is based on a reading of chapters of the book.

Speaking somewhat more formally, in the category of complexes an object and its resolution are not always isomorphic, but the complexes can be altered to repair this defect. In sheaf theory, a similar issue arises in that a surjection of sheaves will not in general be surjective on local sections, i. D-branes are in general classified by twisted K-theory, but RR-fluxes are not quite classified by K-theory since the K-theory classification is incompatible with S-duality in Type II-B string theory.

Chern-Simons gauge theory as a string theory – Witten, Edward Prog. 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. Add both to Cart Add both to List. Nonlinear instantons from supersymmetric p-branes – Marino, Marcos et al. Superschool on Derived Categories and D-branes: Join our email list. Amazon Rapids Fun stories for kids on the go. 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.

Looking for beautiful books? This is supposed to classify the subset of RR field strengths that can exist in the absence of D-branes up mirro equivalence by large gauge transformations. 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 Ships from and sold by Amazon.

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Clay Mathematics Monographs Book 4 Hardcover: As expected, quivers form a category over a given field and wherein one can take speak of the vertex of a direct sum and the linear transformation of a direct sum of quivers.

The physical existence conditions for branes are then discussed and compared dirichket the context of mirror symmetry, culminating in Bridgeland’s definition of stability structures, and its applications to the McKay correspondence and quantum geometry. Amazon Advertising Find, attract, and engage customers.

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 symjetry, presenting an updated discussion that includes subsequent developments. 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. Publication Month and Year: B UTTG Shopbop Designer Fashion Brands.