Truncated affine Rozansky-Witten models as extended TQFTs. (English) Zbl 1522.81176
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.
MSC:
| 81T10 | Model quantum field theories |
| 81T50 | Anomalies in quantum field theory |
| 55N22 | Bordism and cobordism theories and formal group laws in algebraic topology |
| 81P16 | Quantum state spaces, operational and probabilistic concepts |
| 81V05 | Strong interaction, including quantum chromodynamics |
| 13A35 | Characteristic \(p\) methods (Frobenius endomorphism) and reduction to characteristic \(p\); tight closure |
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