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String-net construction of RCFT corr...

Fuchs, Jurgen.

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String-net construction of RCFT correlators

Record Type:	Electronic resources : Monograph/item
Title/Author:	String-net construction of RCFT correlators/ by Jurgen Fuchs, Christoph Schweigert, Yang Yang.
Author:	Fuchs, Jurgen.
other author:	Schweigert, Christoph.
Published:	Cham :Springer International Publishing : : 2022.,
Description:	x, 123 p. :ill., digital ;24 cm.
[NT 15003449]:	Introduction -- Correlators in rational conformal field theory -- Correlators from string nets -- Correlators of particular interest -- Braided Eckmann-Hilton relation -- Universal correlators -- Appendix.
Contained By:	Springer Nature eBook
Subject:	String models - Mathematics. -
Online resource:	https://doi.org/10.1007/978-3-031-14682-4
ISBN:	9783031146824

String-net construction of RCFT correlators
Fuchs, Jurgen.

String-net construction of RCFT correlators[electronic resource] /by Jurgen Fuchs, Christoph Schweigert, Yang Yang. - Cham :Springer International Publishing :2022. - x, 123 p. :ill., digital ;24 cm. - SpringerBriefs in mathematical physics,v. 452197-1765 ;. - SpringerBriefs in mathematical physics ;v. 45..

Introduction -- Correlators in rational conformal field theory -- Correlators from string nets -- Correlators of particular interest -- Braided Eckmann-Hilton relation -- Universal correlators -- Appendix.

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.

ISBN: 9783031146824

Standard No.: 10.1007/978-3-031-14682-4doiSubjects--Topical Terms:

3528332
String models
--Mathematics.

LC Class. No.: QC794.6.S85 / F83 2022

Dewey Class. No.: 539.7258

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490 1 $a SpringerBriefs in mathematical physics, $x 2197-1765 ; $v v. 45
505 0 $a Introduction -- Correlators in rational conformal field theory -- Correlators from string nets -- Correlators of particular interest -- Braided Eckmann-Hilton relation -- Universal correlators -- Appendix.
520 $a 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.
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700 1 $a Schweigert, Christoph. $3 595332
700 1 $a Yang, Yang. $3 1030201
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