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 . 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 3 Label: K-theory and twisted K-theory: Between two of these objects, the maps are regular morphisms, while from the third object to one other it shifts the degree of the other object by one.
This can be extended to RR potentials using differential K-theory. Braid dirichket actions on derived categories of coherent sheaves – Seidel, Paul et brans. A new string revolution in the mids brought the notion of branes to the forefront.
Amazon Rapids Fun stories for kids on the go. 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.
If A is an Abelian category the quasi-morphisms become isomorphic. Abelian categories and derived categories: A natural question to ask here is if a cohomology classification is in anyway tenable since Type II strings in the classical limit is Type II supergravity wherein the RR field strengths are differential forms. D-branes are in general classified by twisted K-theory, but Symmerty are not quite classified by K-theory since the K-theory classification is incompatible with S-duality in Type II-B string theory.
This can be generalized to the Fourier-Mukai transform, which is very important and is used extensively in this book. This is different from the situation in K-theory, where a brane-antibrane pair cancels if all open strings to them cancel out of mirro Q-homology, i. There’s a problem loading this menu right now. Print Price 1 Label: This review is based on a reading of chapters of the book.
The notion of pi-stability can be viewed as arising when asking whether there is a generalization of the theta- and mu-stability conditions that is valid everywhere in the moduli space but reduces to these conditions in the corresponding dirrichlet. Print Price 2 Label: The book first introduces the notion of Dirichlet brane in the context symmettry topological quantum field theories, and then reviews the basics of string theory. Visit our Beautiful Books page and find lovely books for kids, photography lovers and more.
However, there are stable but non-BPS states that exist in the weak coupling regime and they become D-branes at strong coupling. 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.
The notion of a mapping cone comes from algebraic topology, where there is no notion of a kernel or morror in the homotopy category of topological spaces. This motivates the construction of the bounded derived category of coherent sheaves, with the category of coherent sheaves being a subcategory. These developments have led to a great deal of new mathematical work.
Unitarity, D-brane dynamics and D-brane categories – Lazaroiu, C. I’d like to read this book on Kindle Don’t have a Kindle? The authors do not always explain everything they write down in the book, but by consulting the many references the omissions can be filled in if time is not a severe constraint. Goodreads is the world’s largest site for readers with over 50 million reviews.
The notion of pi-stability reduces to theta-stability at orbifold points and mu-stability at the large volume limit, as required.
[math/] Dirichlet branes, homological mirror symmetry, and stability
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. Ssymmetry implies the use of the Hodge star, which depends on the metric and is continuously valued.
A new string revolution in the mids brought the notion of branes to the forefront. The notion of a t-structure is used to detect different Abelian categories inside a derived category. Clay Mathematics Monographs Volume: Amazon Advertising Find, attract, and engage customers.
Description Research in string theory has generated a rich interaction with algebraic geometry, with exciting new work that includes the Strominger-Yau-Zaslow conjecture.
See our librarian page for additional eBook ordering options. The essential philosophy of derived categories is to retain as much as possible the information braness in the complexes, i. Related to quivers are the famous Kac-Moody algebras in that if Symmerty is a quiver then the set of dimension vectors of indecomposable representations of Q does not depend on the orientation of arrows in Q, and the dimension vectors of indecomposable representations correspond to positive roots of the corresponding root system.
The ‘mapping cone’ construction gives a generalization of the kernel and cokernel in the form of an exact triangle of maps between three firichlet. The Clay School on Geometry and String Theory set out to bridge this gap, aymmetry this monograph builds on the expository lectures given there to provide an up-to-date discussion including subsequent developments.
The Poincare bundle induces equivalences between the derived category of an abelian variety and its dual. This site is also available in the following languages: Research in string theory over the last several decades has yielded a rich interaction with algebraic geometry. Geometric Structures and Dualities.
Dirichlet branes, homological mirror symmetry, and stability – INSPIRE-HEP
Ordering on the AMS Bookstore is limited to individuals for personal use only. This is what derived categories do, and so every time the notion of a sub-object is needed, one can find a replacement that uses only the triangulated structure. ComiXology Thousands of Digital Comics. Nonlinear instantons from supersymmetric p-branes – Marino, Marcos et al.
Dirichlet Branes and Mirror Symmetry
The Geometrization Conjecture John Morgan. Book ratings by Goodreads. Graduate students and research mathematicians interested in mathematical aspects of quantum field theory, in particular string theory and mirror symmetry.
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