String-net construction of RCFT correlators / Jürgen Fuchs, Christoph Schweigert, Yang Yang.
Fuchs, Jürgen, 1957 May 19- author.; Schweigert, Christoph. author.; Yang, Yang. author.
2022
QC794.6.S85 F83 2022
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Title String-net construction of RCFT correlators / Jürgen Fuchs, Christoph Schweigert, Yang Yang.
Author Fuchs, Jürgen, 1957 May 19- author.
ISBN 9783031146824 (electronic bk.)
3031146824 (electronic bk.)
3031146816
9783031146817
DOI https://doi.org/10.1007/978-3-031-14682-4
Published Cham, Switzerland : Springer, [2022]
Language English
Description 1 online resource : illustrations.
Item Number 10.1007/978-3-031-14682-4 doi
Call Number QC794.6.S85 F83 2022
Dewey Decimal Classification 539.7/258
Summary This book studies using string-net models to accomplish a direct, purely two-dimensional, approach to correlators of two-dimensional rational conformal field theories. The authors obtain concise geometric expressions for the objects describing bulk and boundary fields in terms of idempotents in the cylinder category of the underlying modular fusion category, comprising more general classes of fields than is standard in the literature. Combining these idempotents with Frobenius graphs on the world sheet yields string nets that form a consistent system of correlators, i.e. a system of invariants under appropriate mapping class groups that are compatible with factorization. The authors extract operator products of field objects from specific correlators; the resulting operator products are natural algebraic expressions that make sense beyond semisimplicity. They also derive an Eckmann-Hilton relation internal to a braided category, thereby demonstrating the utility of string nets for understanding algebra in braided tensor categories. Finally, they introduce the notion of a universal correlator. This systematizes the treatment of situations in which different world sheets have the same correlator and allows for the definition of a more comprehensive mapping class group.
Bibliography, etc. Note Includes bibliographical references.
Access Note Access limited to authorized users.
Source of Description Description based on print version record.
Added Author Schweigert, Christoph. author.
Yang, Yang. author.
Series SpringerBriefs in mathematical physics ; v. 45.
Available in Other Form STRING-NET CONSTRUCTION OF RCFT CORRELATORS.
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Introduction
Correlators in rational conformal field theory
Correlators from string nets
Correlators of particular interest
Braided Eckmann-Hilton relation
Universal correlators
Appendix.

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