Clader E., Ruan Y. (Eds.) B-Model Gromov-Witten Theory

Springer, 2019. — 635 p. — (Trends in Mathematics). — ISBN: 978-3-319-94219-3.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 Constructions
The B-Model Approach to Topological String Theory on Calabi-Yau n-Folds
Geometric Quantization with Applications to Gromov-Witten Theory
Some Classical/Quantum Aspects of Calabi-Yau Moduli
Eynard-Orantin B-Model and Its Application in Mirror Symmetry
The Total Ancestor Potential in Singularity Theory
Lecture Notes on Bihamiltonian Structures and Their Central Invariants