3-dimensional defect TQFTs and their tricategories

Autor(en)

Nils Carqueville, Catherine Meusburger, Gregor Schaumann

Abstrakt

We initiate a systematic study of 3-dimensional 'defect' topological quantum field theories, that we introduce as symmetric monoidal functors on stratified and decorated bordisms. For every such functor we construct a tricategory with duals, which is the natural categorification of a pivotal bicategory. This captures the algebraic essence of defect TQFM, and it gives precise meaning to the fusion of line and surface defects as well as their duality operations. As examples, we discuss how Reshetikhin-Turaev and Turaev-Viro theories embed into our framework, and how they can he extended to defect TQFTs. (C) 2020 Elsevier Inc. All rights reserved.

Organisation(en)

Mathematische Physik

Externe Organisation(en)

Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Julius-Maximilians-Universität Würzburg

Journal

Advances in Mathematics

Band

364

Anzahl der Seiten

58

ISSN

0001-8708

DOI

https://doi.org/10.1016/j.aim.2020.107024

Publikationsdatum

03-2016

Peer-reviewed

Ja

ÖFOS 2012

103024 Quantenfeldtheorie, 101001 Algebra, 103019 Mathematische Physik

Schlagwörter

ASJC Scopus Sachgebiete

Allgemeine Mathematik

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/8cfa759c-6356-4554-80b6-13aaacbb4bc9