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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Description Research in string theory has generated a rich interaction with algebraic geometry, with exciting new work that includes the Strominger-Yau-Zaslow conjecture. Research in string theory over the last several decades has yielded a rich interaction with algebraic geometry.
Dirichlet branes, homological mirror symmetry, and stability – INSPIRE-HEP
The Geometrization Conjecture John Morgan. Print Price 3 Label: Fukaya categories may not have a triangulated structure, so there is a need to add “potentially stable” A-branes to the Fukaya category so that dirichley becomes triangulated. Customers who viewed this item also viewed.
The essential philosophy of derived categories is to retain as much as possible the information given in the complexes, i. Discover Prime Book Box for Kids. Amazon Restaurants Food delivery from local restaurants. In somewhat more detail, to classify fluxes nranes a compact dimensional space-time must deal with the fact that RR fluxes are self-dual. Dirichlet Branes and Mirror Symmetry Share this page. Shopbop Designer Fashion Brands.
Mathematics > Symplectic Geometry
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 physical basis for the McKay correspondence.
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Amazon Advertising Find, attract, and engage customers. In sheaf theory, a similar issue arises in that a surjection of sheaves will not in general be surjective on local sections, i. Visit our Beautiful Books page and find lovely books for kids, photography lovers and more. The Poincare bundle induces equivalences between the derived category of an abelian variety and its dual.
For a complex in an Nirror category, there is a notion of kernel mlrror cokernel, which may not exist in a general category. On counting special Lagrangian homology ririchlet spheres – Joyce, Dominic Contemp.
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 implies the need for D-branes at generic points in moduli space to have “sub” D-branes, which implies the need for a notion of “subobject” of an object in the category of D-branes. In a derived category then, quasi-isomorphisms are viewed as isomorphisms. Please direct mirrof, comments or concerns to feedback inspirehep.
Orbifold resolution by D-branes – Douglas, Michael R. Related to quivers are the famous Kac-Moody algebras in that if Q 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. These developments have led to a great deal of new mathematical work. As an example, if X and Y are simplicial complexes, then they will have homotopy equivalent geometric realizations X and Y if and only if bfanes can find symnetry simplicial complex Z and maps f: For a point u in the Kahler moduli space, E is ‘pi-semistable’ at u if and only if for every sub-brane E’ of E at u, one has phi E is greater than or equal to phi E’where phi E is related to the central charge Z E, u.
Near an orbifold point the world volume of D-branes is given by quiver gauge theories and D-brane configurations correspond to representations of quivers which satisfy the F-flatness and D-flatness conditions.
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Dirichlet Branes and Mirror Symmetry : Bennett Chow :
Goodreads is the world’s largest site for readers with over 50 million reviews. The mapping cone symemtry 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.
However, kernels and cokernels between coherent sheaves will be coherent. The group of distinguished mathematicians and mathematical physicists who produced this monograph worked as a team to create a unique volume.
Calabi-Yau moduli space, mirror manifolds and space-time topology change in string theory – Aspinwall, Paul S. A bounded t-structure is determined by its ‘heart’. Amazon Inspire Digital Educational Resources. Intertwining operator superalgebras and vertex tensor categories for superconformal algebras.
K-theory and twisted K-theory: In this context, a binding process can be viewed as a formation, wherein two D-branes can bind together via a potentially tachyonic open string. The Best Books of The derived category goes beyond K-theory in that it keeps brane of all massless fermionic open strings between a pair of D-branes.
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.