Truncated affine Rozansky--Witten models as extended TQFTs

Abstract

We construct extended TQFTs associated to Rozansky--Witten models with target manifolds $T^{\ast }{\mathbb{C}}^n$. 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.

arXiv comment50 pages; v2: some typos corrected

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Cited by in corpus (2)

• Higher categories of push-pull spans, I: Construction and applications
• Truncated affine Rozansky--Witten models as extended defect TQFTs