TL;DR
This paper explores the mathematical structures of gerbes and line bundles, linking them to anomalies in quantum field theory, particularly focusing on the Weyl fermion vacuum bundle and the Schwinger term.
Contribution
It introduces a framework using trivial line bundles to realize gerbes and connects 1-gerbes to the Weyl fermion vacuum bundle and anomalies.
Findings
Gerbes can be realized through sets of trivial line bundles.
The Weyl fermion vacuum bundle naturally exhibits a 1-gerbe structure.
The Schwinger term acts as an obstruction to triviality of the 1-gerbe.
Abstract
We use sets of trivial line bundles for the realization of gerbes. For 1-gerbes the structure arises naturally for the Weyl fermion vacuum bundle at a fixed time. The Schwinger term is an obstruction in the triviality of a 1-gerbe.
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