On Atiyah-Segal axioms for Witten-type TQFTs

TL;DR

This paper redefines the trace-map bordism in the Atiyah-Segal framework for Witten-type TQFTs, establishing unitarity and proposing a self-consistent modified bordism category for these topological quantum field theories.

Contribution

It introduces a new definition of the trace-map bordism for Witten-type TQFTs and demonstrates their unitarity within this revised framework.

Findings

Witten-type TQFTs are shown to be unitary under the new trace-map definition.

The paper conjectures the self-consistency of the modified bordism category.

A revised Atiyah-Segal framework is proposed for these theories.

Abstract

In this paper, we propose a new definition of the trace-map bordism within the Atiyah-Segal framework for Witten-type TQFTs constructed from the topological twist of mass-gapped theories. We demonstrate that these Witten-type TQFTs are unitary under this revised definition and conjecture the self-consistency of the modified bordism category.