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 . This is the second of two books that provide the scientific record of the school. The first book, Strings and Geometry, edited by Michael R. 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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Dirichlet branes and mirror symmetry – INSPIRE-HEP
Surveys 59no. D1-braneD3-braneD5-brane.
Request a correction Enlighten Editors: Dr Alastair Craw Deposited On: Langlands dualitygeometric Langlands dualityquantum geometric Langlands duality. The authors were not satisfied to tell their story twice, from separate mathematics and physics points of view.
OrlovMirror symmetry for Del Pezzo surfaces: Although the non-Calabi-Yau case symmetryy be of lesser interest to physics, one can still formulate some mirror symmetry statements for, for instance, Fano manifolds. These developments have led to a great deal of new mathematical work.
Mathematics > Algebraic Geometry
Print Price 2 Label: Maxim Kontsevich, Yan Soibelman, Homological mirror symmetry and torus fibrationsmath. Other books in this series.
Computation via topological recursion in matrix models and all- genus? Green-Schwarz mechanismdifferential string structure. symmdtry
mirror symmetry in nLab
Its overall goal is to explore the physical and mathematical aspects of Dirichlet branes. 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.
Algebraic Geometry, to appear, arXiv: After showing how notions of branes arose in string theory, it turns to an introduction to abd algebraic geometry, sheaf theory, and homological algebra needed to define and work with derived categories. 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 theory and algebraic geometry, presenting an updated discussion that includes subsequent developments.
This site is running on Instiki 0. Inthe introduction of Calabi—Yau manifolds into physics as a way to compactify ten-dimensional space-time has led to exciting cross-fertilization between physics and mathematics, especially with the discovery of mirror diricchlet in 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.
Book ratings by Goodreads. Dirichlet Branes and Mirror Symmetry. The narrative is organized around two principal ideas: The topological A-model can be expressed in terms of symplectic geometry of a variety and the topological B-model can be expressed in terms of the algebraic geometry of a variety.
They also explore the ramifications and current state of the Strominger-Yau-Zaslow conjecture.
Nauk 59no. Last revised on April 11, at 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. Skip to main content Accessibility information. Clay Mathematics Monographs Volume: Looking for beautiful books?
In terms of these the statement of mirror symmetry says dirifhlet passing to mirror CYs exchanges the A-model with the B B -model dirochlet conversely:.