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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In this form mirror symmetry remains a conjecture, not the least because for the moment there is no complete construction of these SCFTs.
Dirichlet Branes and Mirror Symmetry
The narrative is organized around two principal ideas: Research in string theory over the last several decades has yielded a rich interaction with algebraic geometry. The Geometrization Conjecture John Morgan. They relate the ideas to active areas of research that include the McKay correspondence, topological quantum field theory, and stability structures.
Last revised on April 11, at After showing how notions of branes arose in string theory, it turns to an introduction to the algebraic geometry, sheaf theory, and homological algebra needed to define and work with derived categories. A new brands revolution in the mids brought the notion of branes to the forefront. The relation to T-duality was established in.
Dirichlet Branes and Mirror Symmetry. Although the non-Calabi-Yau case may be of lesser interest to physics, one can still formulate some mirror symmetry statements for, for instance, Fano manifolds.
S-dualityelectric-magnetic duality. Publication Month and Year: See our librarian page for additional eBook ordering options. Ballard, Meet homological mirror symmetry arxiv: 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.
Request a correction Enlighten Editors: Graduate students and research mathematicians interested in mathematical aspects of quantum field theory, in particular string theory and mirror symmetry.
Dirichlet Branes and Mirror Symmetry Share this page. In terms of these the statement of mirror symmetry says that passing to mirror CYs exchanges the A-model with the B B -model and conversely:.
Visit our Beautiful Books page and find lovely books for kids, photography lovers sirichlet more. Langlands dualitygeometric Langlands dualityquantum geometric Langlands duality. These developments have led to a great deal of new mathematical work.
Instead, theirs is a unified presentation offered in a way that both mathematicians and physicists can follow, without having all of digichlet foundations of both subjects at their immediate disposal.
Mathematics > Algebraic Geometry
Clay mathematics monographs 4. Deriving the matrix model arXiv: Contact us The University of Glasgow is a registered Scottish charity: The authors explain how Kontsevich’s conjecture is equivalent to branee identification of two different categories of Dirichlet branes.
Description Research in string theory has generated a rich interaction with algebraic geometry, with exciting new work that includes the Strominger-Yau-Zaslow conjecture. Join our email list. Seidel, Homological mirror symmetry for the quartic surfacearXiv: Print Price 3 Label: 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.
Dirichlet Branes and Mirror Symmetry – Enlighten: Publications
Paul SeidelHomological mirror symmetry for the genus two curveJ. Abstract This monograph builds on lectures at the Clay School on Geometry and String Theory that sought to bridge xirichlet gap between the languages of string theory and algebraic geometry, presenting an updated discussion that includes subsequent developments.
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