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Dirichlet Branes and Mirror Symmetry (Hardcover)
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Dirichlet Branes and Mirror Symmetry (Hardcover)
Series: Clay Mathematics Monographs
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Research in string theory has generated a rich interaction with
algebraic geometry, with exciting new work that includes the
Strominger-Yau-Zaslow conjecture. This monograph builds on lectures
at the 2002 Clay School on Geometry and String Theory that sought
to bridge the gap between the languages of string theory and
algebraic geometry, presenting an updated discussion that includes
subsequent developments. The group of distinguished mathematicians
and mathematical physicists who produced this monograph worked as a
team to create a unique volume. Its overall goal is to explore the
physical and mathematical aspects of Dirichlet branes. The
narrative is organized around two principal ideas: Kontsevich's
Homological Mirror, Symmetry conjecture, and the
Strominger-Yau-Zaslow conjecture. The authors explain how
Kontsevich's conjecture is equivalent to the identification of two
different categories of Dirichlet branes. They also explore the
ramifications and current state of the Strominger-Yau-Zaslow
conjecture. They relate the ideas to active areas of research that
include the McKay correspondence, topological quantum field theory,
and stability structures. The authors were not satisfied to tell
their story twice, from separate mathematics and physics points of
view. Instead, theirs is a unified presentation offered in a way
that both mathematicians and physicists can follow, without having
all of the foundations of both subjects at their immediate
disposal.
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