Overview
- Restricts readers' attention to the best-known example of mirror symmetry: a quintic hypersurface in CP^4
- Explains mirror symmetry from the point of view of a researcher involved in physics and mathematics
- Provides a detailed exposition of the procedure of computation in the last two chapters
Part of the book series: SpringerBriefs in Mathematical Physics (BRIEFSMAPHY, volume 29)
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Table of contents (5 chapters)
Keywords
About this book
First, there is a brief review of the process of discovery of mirror symmetry and the striking result proposed in the celebrated paper by Candelas and his collaborators. Next, some elementary results of complex manifolds and Chern classes needed for study of mirror symmetry are explained. Then the topological sigma models, the A-model and the B-model, are introduced. The classical mirror symmetry hypothesis is explained as the equivalence between the correlation function of the A-model of a quintic hyper-surface and that of the B-model of its mirror manifold.
On the B-model side, the process of construction of a pair of mirror Calabi–Yau threefold using toric geometry is briefly explained. Also given are detailed explanations of the derivation of the Picard–Fuchs differential equation of the period integrals and on the process of deriving the instanton expansion of the A-model Yukawa coupling based on the mirror symmetry hypothesis.
On the A-model side, the moduli space of degree d quasimaps from CP^1 with two marked points to CP^4 is introduced, with reconstruction of the period integrals used in the B-model side as generating functions of the intersection numbers of the moduli space. Lastly, a mathematical justification for the process of the B-model computation from the point of view of the geometry of the moduli space of quasimaps is given.
The style of description is between that of mathematics and physics, with the assumption that readers have standard graduate student backgrounds in both disciplines.
Reviews
“Graduate students – or other researchers – in theoretical physics with an interest in the mathematical aspects of mirror symmetry form a natural audience for this text.” (Thomas Prince, zbMATH 1431.14034, 2020)
Authors and Affiliations
Bibliographic Information
Book Title: Classical Mirror Symmetry
Authors: Masao Jinzenji
Series Title: SpringerBriefs in Mathematical Physics
DOI: https://doi.org/10.1007/978-981-13-0056-1
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd., part of Springer Nature 2018
Softcover ISBN: 978-981-13-0055-4Published: 26 April 2018
eBook ISBN: 978-981-13-0056-1Published: 18 April 2018
Series ISSN: 2197-1757
Series E-ISSN: 2197-1765
Edition Number: 1
Number of Pages: VIII, 140
Topics: Mathematical Physics, Quantum Field Theories, String Theory