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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.
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