String-net construction of RCFT correlators / Jürgen Fuchs, Christoph Schweigert, Yang Yang.

Format:

Book

Author/Creator:

Fuchs, Jürgen, 1957 May 19- author.

Schweigert, Christoph, author.

Yang, Yang., author.

Series:

SpringerBriefs in mathematical physics ; v. 45.

SpringerBriefs in mathematical physics ; volume 45

Language:

English

Subjects (All):

String models--Mathematics.

String models.

Lie groups.

Quantum field theory.

Physical Description:

1 online resource : illustrations.

Place of Publication:

Cham, Switzerland : Springer, [2022]

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.

Contents:

Introduction

Correlators in rational conformal field theory

Correlators from string nets

Correlators of particular interest

Braided Eckmann-Hilton relation

Universal correlators

Appendix.

Notes:

Includes bibliographical references.

Print version record.

Other Format:

Print version: SCHWEIGERT, CHRISTOPH. FUCHS, JURGEN. YANG, YANG. STRING-NET CONSTRUCTION OF RCFT CORRELATORS.

ISBN:

9783031146824

3031146824

OCLC:

1360434866

Access Restriction:

Restricted for use by site license.