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arXiv · 2201.03284

Truncated affine Rozansky--Witten models as extended TQFTs

Ilka Brunner·Nils Carqueville·Daniel Roggenkamp
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Abstract

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.

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Ilka Brunner, Nils Carqueville, Daniel Roggenkamp. 2022-01-10. Truncated affine Rozansky--Witten models as extended TQFTs. https://doi.org/10.1007/s00220-022-04614-4

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