Functorial QFT, Gauge Anomalies and the Dirac Determinant Bundle

TL;DR

This paper develops an axiomatic quantum field theory framework using the determinant line bundle to model fermionic path integrals, elucidating gauge anomalies through a functorial approach and algebraic sewing laws.

Contribution

It introduces a functorial construction of quantum field theory based on the determinant line bundle, linking gauge anomalies to algebraic sewing laws in a novel way.

Findings

Fock space functor models fermionic path integrals.

Sewing axiom corresponds to algebraic pasting law for Dirac determinants.

Representation of boundary gauge group explains gauge anomalies.

Abstract

Using properties of the determinant line bundle for a family of elliptic boundary value problems, we explain how the Fock space functor defines an axiomatic quantum field theory which formally models the Fermionic path integral. The 'sewing axiom' of the theory arises as an algebraic pasting law for the determinant of the Dirac operator. We show how representations of the boundary gauge group fit into this description and that this leads to a Fock functor description of certain gauge anomalies.