Truncated affine Rozansky--Witten models as extended TQFTs

Abstract

We construct extended TQFTs associated to Rozansky-Witten models with target manifolds T * 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 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 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. 2-categories of truncated affineRozansky-Witten models

A Panorama Of Physical Mathematics c. 2022

“…(These are also known as B-twisted 3d N = 4 sigma models.) Recently interesting progress has been made on such theories associated with noncompact manifolds such as Coulomb branches of 3d N = 4 theories [908][909][910]. These investigations are part of a program to give a physical framework for the non-semisimple 3-manifold invariants discussed in [911][912][913][914].…”