© 2018

B-Model Gromov-Witten Theory

  • Emily Clader
  • Yongbin Ruan


  • 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 Trends in Mathematics book series (TM)

Table of contents

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 integrable systems.


mirror symmetry quantization singularity theory integrable systems holomorphic anomaly equation modularity polyvector fields primitive forms Givental’s ancestor potential

Editors and affiliations

  • Emily Clader
    • 1
  • Yongbin Ruan
    • 2
  1. 1.San Francisco State UniversitySan FranciscoUSA
  2. 2.University of MichiganAnn ArborUSA

Bibliographic information

  • Book Title B-Model Gromov-Witten Theory
  • Editors Emily Clader
    Yongbin Ruan
  • Series Title Trends in Mathematics
  • Series Abbreviated Title Trends in Math.
  • DOI
  • Copyright Information Springer Nature Switzerland AG 2018
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-319-94219-3
  • eBook ISBN 978-3-319-94220-9
  • 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
  • Buy this book on publisher's site
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