| Full text | |
| Author(s): |
Bunk, Severin
[1]
;
Saemann, Christian
;
Szabo, Richard J.
Total Authors: 3
|
| Affiliation: | [1] Heriot Watt Univ, Dept Math, Colin Maclaurin Bldg, Edinburgh EH14 4AS, Midlothian - Scotland
Total Affiliations: 1
|
| Document type: | Review article |
| Source: | REVIEWS IN MATHEMATICAL PHYSICS; v. 30, n. 1 FEB 2018. |
| Web of Science Citations: | 4 |
| Abstract | |
We construct a prequantum 2-Hilbert space for any line bundle gerbe whose Dixmier-Douady class is torsion. Analogously to usual prequantization, this 2-Hilbert space has the category of sections of the line bundle gerbe as its underlying 2-vector space. These sections are obtained as certain morphism categories in Waldorf's version of the 2-category of line bundle gerbes. We show that these morphism categories carry a monoidal structure under which they are semisimple and abelian. We introduce a dual functor on the sections, which yields a closed structure on the morphisms between bundle gerbes and turns the category of sections into a 2-Hilbert space. We discuss how these 2-Hilbert spaces fit various expectations from higher prequantization. We then extend the transgression functor to the full 2-category of bundle gerbes and demonstrate its compatibility with the additional structures introduced. We discuss various aspects of Kostant-Souriau prequantization in this setting, including its dimensional reduction to ordinary prequantization. (AU) | |
| FAPESP's process: | 16/04341-5 - Classical and quantum aspects of field theory on non-geometric backgrounds |
| Grantee: | Vladislav Kupriyanov |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - International |