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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Mathematics > Symplectic Geometry

Author s Product display: AmazonGlobal Ship Orders Internationally. Intertwining operator superalgebras and vertex tensor categories for superconformal algebras.

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.

Withoutabox Submit to Film Festivals. 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 algebraic geometry in a coherent logical context. But topologically distinct RR field strengths can exist in configurations free of branes, and so the integral cohomology is too large.

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. Amazon Second Chance Pass it on, trade it in, give it a second life. The K-theory classification classifies the allowed RR field strengths as well as the charges of stable D-branes. Amazon Giveaway allows you to run promotional giveaways in order to create buzz, reward your audience, and attract new followers and customers.

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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. Research in string theory over the last several decades has yielded a rich interaction with algebraic geometry.


D-branes in Gepner models – Recknagel, A. A Bestiary For Physicists. Print Price 3 Label: The Best Books of In the homotopy category for example it is difficult to say when a sequence of morphisms is exact, and so there is no kernel or cokernel.

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 determines which elements in a derived category actually correspond to physical BPS D-branes. The notion of a t-structure is used to detect different Abelian categories inside a derived category. Orbifold resolution by D-branes – Douglas, Michael R. Product details Format Hardback pages Dimensions Print Price 1 Label: 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.

Kahler cone substructure – Sharpe, Eric R. Two lectures on D-geometry and noncommutative geometry – Douglas, Michael R. The point is that not all triangles of maps are exact, but that any triangle isomorphic to a distinguished triangle is declared to be exact.

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Dirichlet Branes and Mirror Symmetry : Bennett Chow :

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. 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.

Amazon Advertising Find, attract, and engage customers. An object E’ is a sub-object of an object E if there exists and injective homomorphism from E’ to E. Join our email list. Einstein type metrics and stability on vector bundles – Leung, Naichung Conan J. In somewhat more detail, to classify fluxes on a compact dimensional space-time must deal with the fact that RR fluxes are self-dual.


Mathematics > Algebraic Geometry

A distinguished triangle will not permit the decay of a stable B-brane into two other stable B-branes. Unitarity, D-brane dynamics and D-brane categories – Lazaroiu, C.

Would you like to tell us about a lower price? Share your thoughts with other customers. Clay Mathematics Monographs Volume: 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. This motivates the “twisting” of the NS 3-form field strength, namely the use cirichlet twisted K-theory.

This can be extended wymmetry RR potentials using differential K-theory. If it is not Artinian, then some objects could decay into an infinite number of subjects on the line of marginal stability. However, kernels and cokernels between coherent sheaves will be coherent. This implies that there are no short exact sequences, and to compensate for this, ‘distinguished triangles’ of maps are brought in and a way of shifting complexes up and down.

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. Amazon Restaurants Food delivery from local restaurants. Amazon Rapids Fun stories for kids on the go.