Truncated affine Rozansky--Witten models as extended defect TQFTs

TL;DR

This paper constructs extended topological quantum field theories from affine Rozansky--Witten models using the cobordism hypothesis, explicitly including defects and calculating associated state spaces.

Contribution

It applies the cobordism hypothesis with singularities to affine Rozansky--Witten models, systematically incorporating defects and computing state spaces.

Findings

Homotopy 2-category shown to be pivotal

Explicit graphical calculus developed for 3D models

State spaces computed for surfaces with defect networks

Abstract

We apply the cobordism hypothesis with singularities to the case of affine Rozansky--Witten models, providing a construction of extended TQFTs that includes all line and surface defects. On a technical level, this amounts to proving that the associated homotopy 2-category is pivotal, and to systematically employing its 3-dimensional graphical calculus. This in particular allows us to explicitly calculate state spaces for surfaces with arbitrary defect networks. As specific examples we discuss symmetry defects which can be used to model non-trivial background gauge fields, as well as boundary conditions.