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B-Model Gromov-Witten Theory

  • Book
  • © 2018

Overview

Editors:
  1. Emily Clader

    1. San Francisco State University, San Francisco, USA

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    You can also search for this editor in PubMed   Google Scholar

  2. Yongbin Ruan

    1. University of Michigan, Ann Arbor, USA

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    You can also search for this editor in PubMed   Google Scholar

  • Attempts to close the gap between the mathematical community’s understanding of the B model and the A model
  • Brings together mathematical and physical perspectives in one reference, providing a unique opportunity for the two communities to learn from one another
  • Provides an overview of several methods by which mirrors have been constructed
  • Details the “BCOV” B-model theory from a physical perspective

Part of the book series: Trends in Mathematics (TM)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xiii
    Download chapter PDF

  2. Mirror Symmetry Constructions

    • Emily Clader, Yongbin Ruan
    Pages 1-77

  3. The B-Model Approach to Topological String Theory on Calabi-Yau n-Folds

    • Albrecht Klemm
    Pages 79-397

  4. Geometric Quantization with Applications to Gromov-Witten Theory

    • Emily Clader, Nathan Priddis, Mark Shoemaker
    Pages 399-462

  5. Some Classical/Quantum Aspects of Calabi-Yau Moduli

    • Si Li
    Pages 463-497

  6. Eynard-Orantin B-Model and Its Application in Mirror Symmetry

    • Bohan Fang
    Pages 499-538

  7. The Total Ancestor Potential in Singularity Theory

    • Todor Milanov
    Pages 539-571

  8. Lecture Notes on Bihamiltonian Structures and Their Central Invariants

    • Si-Qi Liu
    Pages 573-625
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Keywords

About this book

This book collects various perspectives, contributed by both mathematicians and physicists, on the B-model and its role in mirror symmetry. Mirror symmetry is an active topic of research in both the mathematics and physics communities, but among mathematicians, the “A-model” half of the story remains much better-understood than the B-model. This book aims to address that imbalance. 

It begins with an overview of several methods by which mirrors have been constructed, and from there, gives a thorough account of the “BCOV” B-model theory from a physical perspective; this includes the appearance of such phenomena as the holomorphic anomaly equation and connections to number theory via modularity. Following a mathematical exposition of the subject of quantization, the remainder of the book is devoted to the B-model from a mathematician’s point-of-view, including such topics as polyvector fields and primitive forms, Givental’s ancestor potential, and integrablesystems.

Editors and Affiliations

  • San Francisco State University, San Francisco, USA

    Emily Clader

  • University of Michigan, Ann Arbor, USA

    Yongbin Ruan

Bibliographic Information

  • Book Title: B-Model Gromov-Witten Theory

  • Editors: Emily Clader, Yongbin Ruan

  • Series Title: Trends in Mathematics

  • DOI: https://doi.org/10.1007/978-3-319-94220-9

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Nature Switzerland AG 2018

  • Hardcover ISBN: 978-3-319-94219-3Published: 18 April 2019

  • eBook ISBN: 978-3-319-94220-9Published: 08 April 2019

  • Series ISSN: 2297-0215

  • Series E-ISSN: 2297-024X

  • Edition Number: 1

  • Number of Pages: XIII, 625

  • Number of Illustrations: 59 b/w illustrations, 6 illustrations in colour

  • Topics: Algebraic Geometry, Mathematical Physics

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