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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Privacy policy Powered by Invenio v1. 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. The authors were not satisfied to tell their story twice, from separate mathematics and physics points of view.

By using our website you agree to our use of cookies. Graduate students and research mathematicians interested in mathematical aspects of quantum field theory, in particular string theory and mirror symmetry. In a derived category the morphisms do not have kernels or cokernels, and so they are ‘additive’ but not Abelian.

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. They also explore the ramifications and current state of the Strominger-Yau-Zaslow conjecture.

If it is not Artinian, then some objects could decay into an infinite number of subjects on the line of marginal stability. There’s a problem loading this menu right now.

Amazon Renewed Refurbished products with a warranty. This motivates the “twisting” of the NS 3-form field strength, namely the use of twisted K-theory.

### Dirichlet Branes and Mirror Symmetry : Bennett Chow :

If a quiver representation is theta-stable then the orbit under the complexified gauge group will contain a solution to the D-flatness conditions. This can be extended to Bbranes potentials using differential K-theory. K theory and Ramond-Ramond charge diriclet Minasian, Ruben et al. Clay Mathematics Monographs Volume: 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.

The physical existence conditions mieror 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.

Print Price 1 Label: Information References 42 Citations 20 Files Plots. 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 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.

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A Bestiary For Physicists. Dirichlet Branes and Mirror Symmetry. 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 Digichletwhere phi E is related to the central charge Z E, u.

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.

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Abelian categories and derived categories: D-branes in Gepner models – Recknagel, A. Withoutabox Submit to Film Festivals. Unitarity, D-brane dynamics and D-brane categories – Lazaroiu, C. Publication Month and Year: 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.

Amazon Giveaway allows you to run promotional giveaways in order to create buzz, reward your audience, and attract new followers and customers. The authors explain how Kontsevich’s conjecture is equivalent to the identification of two different categories of Dirichlet branes. Ordering on the AMS Bookstore is limited to individuals for personal use synmetry. These developments have led to a great deal of new mathematical work.

Author s Product display: This implies symmerty use of the Hodge star, which depends on the metric and is continuously valued.

## Mathematics > Algebraic Geometry

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. Discover Dirichlt Book Box for Kids.

The real roots are dimension vectors for which there is exactly one indecomposable representation, whereas the imaginary roots are the dimension vectors for which there are families of indecomposable representations. We use cookies to give you the best possible experience. One of these items ships sooner than the other. But topologically distinct RR field strengths can exist in configurations free of branes, and so diirichlet integral cohomology is too large. This review is based on a reading of chapters of the book.

The derived category goes beyond K-theory in that it keeps track of all massless fermionic open strings between a pair of D-branes.

## Dirichlet Branes and Mirror Symmetry

Top Reviews Most recent Top Reviews. Giving a fairly detailed overview of mirror symmetry that emphasizes both its mathematical and physical aspects, this book should be accessible to readers who are familiar with topological quantum field theory, superstring theory, and the highly esoteric mathematical constructions used in these fields.

This is what derived categories do, and so symnetry time the notion of a sub-object is needed, one can find a replacement that uses only the triangulated structure.

These conditions are applicable in the ‘large volume limit’ and for D-flatness depends on the complexified gauge group dircihlet the notion of theta-stability at the orbifold points and mu-stability at the large volume limit.