Truncated Affine Rozansky–Witten Models as Extended TQFTs

Autor(en)

Ilka Brunner, Nils Carqueville, Daniel Roggenkamp

Abstrakt

We construct extended TQFTs associated to Rozansky--Witten models with target manifolds $T^*\mathbb{C}^n$. The starting point of the construction is the 3-category whose objects are such Rozansky--Witten models, and whose morphisms are defects of all codimensions. By truncation, we obtain a (non-semisimple) 2-category $\mathcal{C}$ of bulk theories, surface defects, and isomorphism classes of line defects. Through a systematic application of the cobordism hypothesis we construct a unique extended oriented 2-dimensional TQFT valued in $\mathcal{C}$ for every affine Rozansky--Witten model. By evaluating this TQFT on closed surfaces we obtain the infinite-dimensional state spaces (graded by flavour and R-charges) of the initial 3-dimensional theory. Furthermore, we explicitly compute the commutative Frobenius algebras that classify the restrictions of the extended theories to circles and bordisms between them.

Organisation(en)

Mathematische Physik

Externe Organisation(en)

Ludwig-Maximilians-Universität München, Universität Mannheim

Journal

Communications in Mathematical Physics

Band

400

Seiten

371–415

Anzahl der Seiten

45

ISSN

0010-3616

DOI

https://doi.org/10.1007/s00220-022-04614-4

Publikationsdatum

04-2022

Peer-reviewed

Ja

ÖFOS 2012

103019 Mathematische Physik

Schlagwörter

ASJC Scopus Sachgebiete

Statistical and Nonlinear Physics, Mathematical Physics

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/37174768-4503-44e2-bb6f-31e11bccce14