October 14, 2020

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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Chern-Simons gauge theory as a string theory – Witten, Edward Prog. They also explore the ramifications and current state of the Strominger-Yau-Zaslow conjecture. The authors were not satisfied to tell their story twice, from separate mathematics and physics points of view.

We hope it will allow students and researchers who are familiar with the language of one of the two fields to gain acquaintance with the language of the other. K theory and Ramond-Ramond charge – Minasian, Ruben et al. 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.

Mathematics > Symplectic Geometry

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

The group of distinguished mathematicians and mathematical physicists who produced this monograph worked as a team to create a unique volume. The authors explain how Kontsevich’s conjecture is equivalent to the identification of two different categories of Dirichlet branes.


In a derived category the morphisms do not have kernels or cokernels, and so they are ‘additive’ but not Abelian. 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.

But topologically distinct RR field strengths can exist in configurations free of branes, and so the integral cohomology is too large.

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. This is supposed to classify the subset of RR field strengths that can exist in the absence of D-branes up to equivalence by large gauge syymmetry. The Poincare bundle induces equivalences between the derived category of an abelian variety and its dual.

Dirichlet Branes and Mirror Symmetry

Book ratings by Goodreads. The notion of a mapping cone comes from algebraic topology, where there is no notion of a kernel or cokernel in the homotopy category of topological spaces.

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. This implies that there are no short exact sequences, and to compensate for this, ‘distinguished triangles’ of maps are symmehry in and a way of shifting complexes up and down. We’re featuring millions of their reader ratings on our book pages to help you find your new favourite 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 mkrror in the moduli space but reduces to these conditions in the corresponding limits.


A new string symmetrt in the mids brought the notion of branes to the forefront. In a derived category then, quasi-isomorphisms are viewed as isomorphisms.

Dirichlet branes and mirror symmetry – INSPIRE-HEP

Calabi-Yau moduli space, mirror manifolds and space-time topology change in string theory – Aspinwall, Paul S. In sheaf theory, a similar issue arises in that a surjection of sheaves will not in general be surjective on local sections, i.

Fukaya categories may not have a triangulated structure, so there is a need to add “potentially stable” A-branes to the Fukaya category so miror it becomes triangulated. Amazon Music Stream millions of songs. Amazon Inspire Digital Educational Resources.

[math/] Dirichlet branes, homological mirror symmetry, and stability

Print Price 3 Label: Write a customer review. One of these items ships sooner than the other. Of great research interest but not discussed in too much detail in this book is the connection between K-theory and S-duality.

Braid group actions on derived categories of coherent sheaves – Seidel, Paul et al. The notion of pi-stability reduces to theta-stability at orbifold points and mu-stability at the large volume limit, as required.