Truncated affine Rozansky--Witten models as extended TQFTs

TL;DR

This paper constructs extended 2D topological quantum field theories from Rozansky--Witten models with target space $T^*C^n$, providing explicit algebraic structures and state spaces for these theories.

Contribution

It introduces a systematic construction of extended TQFTs from affine Rozansky--Witten models using the cobordism hypothesis, including explicit algebraic classifications.

Findings

Constructed extended TQFTs for Rozansky--Witten models with target $T^*C^n$

Derived infinite-dimensional state spaces graded by flavor and R-charges

Explicitly computed Frobenius algebras for circle and bordism restrictions

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.