Truncated affine Rozansky--Witten models as extended TQFTs

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-s...

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Bibliographic Details
Published in:arXiv.org 2022-01
Main Authors: Brunner, Ilka, Carqueville, Nils, Roggenkamp, Daniel
Format: Article
Language:English
Subjects:
Dislocations
Flavors
Isomorphism
Surface defects
Two dimensional models
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2201.03284