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Lectures on Tensor Categories and Modular Functors (Paperback)
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Lectures on Tensor Categories and Modular Functors (Paperback)
Series: University Lecture Series
Expected to ship within 12 - 19 working days
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This book gives an exposition of the relations among the following
three topics: monoidal tensor categories (such as a category of
representations of a quantum group), 3-dimensional topological
quantum field theory, and 2-dimensional modular functors (which
naturally arise in 2-dimensional conformal field theory). The
following examples are discussed in detail the category of
representations of a quantum group at a root of unity and the
Wess-Zumino-Witten modular functor. The idea that these topics are
related first appeared in the physics literature in the study of
quantum field theory. Pioneering works of Witten and Moore-Seiberg
triggered an avalanche of papers, both physical and mathematical,
exploring various aspects of these relations.Upon preparing to
lecture on the topic at MIT, however, the authors discovered that
the existing literature was difficult and that there were gaps to
fill. The text is wholly expository and finely succinct. It gathers
results, fills existing gaps, and simplifies some proofs. The book
makes an important addition to the existing literature on the
topic. It would be suitable as a course text at the
advanced-graduate level.
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