English

A GNS construction of three-dimensional abelian Dijkgraaf-Witten theories

Quantum Algebra 2017-12-11 v2 High Energy Physics - Theory Mathematical Physics math.MP

Abstract

We give a detailed account of the so-called "universal construction" that aims to extend invariants of closed manifolds, possibly with additional structure, to topological field theories and show that it amounts to a generalization of the GNS construction. We apply this construction to an invariant defined in terms of the groupoid cardinality of groupoids of bundles to recover Dijkgraaf-Witten theories, including the vector spaces obtained as a linearization of spaces of principal bundles.

Keywords

Cite

@article{arxiv.1703.05018,
  title  = {A GNS construction of three-dimensional abelian Dijkgraaf-Witten theories},
  author = {Lukas Müller and Christoph Schweigert},
  journal= {arXiv preprint arXiv:1703.05018},
  year   = {2017}
}

Comments

17 pages, 4 figures, v2: typos corrected