Mirror Symmetry

Mirror Symmetry
Author :
Publisher : American Mathematical Soc.
Total Pages : 954
Release :
ISBN-10 : 9780821829554
ISBN-13 : 0821829556
Rating : 4/5 (54 Downloads)

Book Synopsis Mirror Symmetry by : Kentaro Hori

Download or read book Mirror Symmetry written by Kentaro Hori and published by American Mathematical Soc.. This book was released on 2003 with total page 954 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thorough and detailed exposition is the result of an intensive month-long course on mirror symmetry sponsored by the Clay Mathematics Institute. It develops mirror symmetry from both mathematical and physical perspectives with the aim of furthering interaction between the two fields. The material will be particularly useful for mathematicians and physicists who wish to advance their understanding across both disciplines. Mirror symmetry is a phenomenon arising in string theory in which two very different manifolds give rise to equivalent physics. Such a correspondence has significant mathematical consequences, the most familiar of which involves the enumeration of holomorphic curves inside complex manifolds by solving differential equations obtained from a ``mirror'' geometry. The inclusion of D-brane states in the equivalence has led to further conjectures involving calibrated submanifolds of the mirror pairs and new (conjectural) invariants of complex manifolds: the Gopakumar-Vafa invariants. This book gives a single, cohesive treatment of mirror symmetry. Parts 1 and 2 develop the necessary mathematical and physical background from ``scratch''. The treatment is focused, developing only the material most necessary for the task. In Parts 3 and 4 the physical and mathematical proofs of mirror symmetry are given. From the physics side, this means demonstrating that two different physical theories give isomorphic physics. Each physical theory can be described geometrically, and thus mirror symmetry gives rise to a ``pairing'' of geometries. The proof involves applying $R\leftrightarrow 1/R$ circle duality to the phases of the fields in the gauged linear sigma model. The mathematics proof develops Gromov-Witten theory in the algebraic setting, beginning with the moduli spaces of curves and maps, and uses localization techniques to show that certain hypergeometric functions encode the Gromov-Witten invariants in genus zero, as is predicted by mirror symmetry. Part 5 is devoted to advanced topi This one-of-a-kind book is suitable for graduate students and research mathematicians interested in mathematics and mathematical and theoretical physics.


Mirror Symmetry Related Books

Mirror Symmetry
Language: en
Pages: 954
Authors: Kentaro Hori
Categories: Mathematics
Type: BOOK - Published: 2003 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

This thorough and detailed exposition is the result of an intensive month-long course on mirror symmetry sponsored by the Clay Mathematics Institute. It develop
Differential Geometry and Mathematical Physics
Language: en
Pages: 766
Authors: Gerd Rudolph
Categories: Science
Type: BOOK - Published: 2012-11-09 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential
Symplectic Geometry and Mathematical Physics
Language: en
Pages: 504
Authors: P. Donato
Categories: Mathematics
Type: BOOK - Published: 1991-12 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

This volume contains the proceedings of the conference "Colloque de Goometrie Symplectique et Physique Mathematique" which was held in Aix-en-Provence (France),
A Course in Modern Mathematical Physics
Language: en
Pages: 620
Authors: Peter Szekeres
Categories: Mathematics
Type: BOOK - Published: 2004-12-16 - Publisher: Cambridge University Press

DOWNLOAD EBOOK

This textbook, first published in 2004, provides an introduction to the major mathematical structures used in physics today.
Physics for Mathematicians
Language: en
Pages: 733
Authors: Michael Spivak
Categories: Mechanics
Type: BOOK - Published: 2010 - Publisher:

DOWNLOAD EBOOK