Extended TQFTs From Non-Semisimple Modular Categories

TL;DR

This paper develops 3D extended topological quantum field theories from non-semisimple modular categories, explicitly describing their associated categories and functors, and showing the circle category corresponds to projective objects, which may not be semisimple.

Contribution

It constructs ETQFTs from non-semisimple modular categories and characterizes their associated categories, expanding the scope beyond semisimple cases.

Findings

Circle category is equivalent to the subcategory of projective objects.

The construction applies to non-semisimple modular categories.

Explicit identification of linear categories and functors in the ETQFTs.

Abstract

We construct 3-dimensional once-Extended Topological Quantum Field Theories (ETQFTs for short) out of (possibly non-semisimple) modular categories, and we explicitly identify linear categories and functors in their image. The circle category of an ETQFT produced by our construction is equivalent to the full subcategory of projective objects of the underlying modular category. In particular, it need not be semisimple.