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String-Net Construction of RCFT Correlators

Part of the SpringerBriefs in Mathematical Physics Book Series (volume 45)

DOI: 10.1007/978-3-031-14682-4

ISBN: 978-3-031-14681-7

Publisher: Springer International Publishing - Springer Journals

Jan 2, 2023

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Chapter 1Introduction

Fuchs, Jürgen; Schweigert, Christoph; Yang, Yang

Pages: 1 –7

[The main topic of this book is a novel construction of the correlators of two-dimensional rational conformal field theories on arbitrary world sheets, allowing in particular for physical boundaries as well as for defects and general defect junctions.]
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Chapter 2Correlators in Rational Conformal Field Theory

Fuchs, Jürgen; Schweigert, Christoph; Yang, Yang

Pages: 9 –34

[In this chapter we turn the physics task of finding correlation functions into the mathematically precise problem of determining specific elements in spaces of conformal blocks. These spaces are described in terms of an open-closed modular functor.]
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Chapter 3Correlators from String Nets

Fuchs, Jürgen; Schweigert, Christoph; Yang, Yang

Pages: 35 –59

[This chapter contains our central construction, the one of string-net correlators, as defined in Definition 3.26. The chief result—Theorem 3.28—states that the construction does provide a consistent system of correlators.]
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Chapter 4Correlators of Particular Interest

Fuchs, Jürgen; Schweigert, Christoph; Yang, Yang

Pages: 61 –84

[The prescription presented in the previous chapter applies to all correlators of the theory. However, a few specific correlators are of particular interest; concretely, partition functions on the one hand, and correlators which determine operator products, i.e. composition morphisms on the field...
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Chapter 5Internal Eckmann–Hilton Relation

Fuchs, Jürgen; Schweigert, Christoph; Yang, Yang

Pages: 85 –93

[The exchange law for ordinary natural transformations turns out to have an analogue for internal natural transformations. To obtain this analogue, which we call the internal Eckmann–Hilton relation, we introduce three braided colored operads. The string-net correlator defined in Sect. 3.5...
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Chapter 6Outlook: Universal Correlators

Fuchs, Jürgen; Schweigert, Christoph; Yang, Yang

Pages: 95 –100

[It can happen that two world sheets with different defect networks and thus different defect patterns—that is, assignments of labels to the cells of the world sheet—turn out to have the same correlator. Existing approaches to correlators, including the string-net construction considered in the...

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