Gauge theory on noncommutative Riemannian principal bundles
| dc.contributor.author | Ćaćić, Branimir | |
| dc.contributor.author | Mesland, Bram | |
| dc.date.accessioned | 2023-11-22T14:32:16Z | |
| dc.date.available | 2023-11-22T14:32:16Z | |
| dc.date.issued | 2021-10-11 | |
| dc.description.abstract | We present a new, general approach to gauge theory on principal G-spectral triples, where G is a compact connected Lie group. We introduce a notion of vertical Riemannian geometry for G-C∗-algebras and prove that the resulting noncommutative orbitwise family of Kostant’s cubic Dirac operators defines a natural unbounded K K G-cycle in the case of a principal G-action. Then, we introduce a notion of principal G-spectral triple and prove, in particular, that any such spectral triple admits a canonical factorisation in unbounded K K G-theory with respect to such a cycle: up to a remainder, the total geometry is the twisting of the basic geometry by a noncommutative superconnection encoding the vertical geometry and underlying principal connection. Using these notions, we formulate an approach to gauge theory that explicitly generalises the classical case up to a groupoid cocycle and is compatible in general with this factorisation; in the unital case, it correctly yields a real affine space of noncommutative principal connections with affine gauge action. Our definitions cover all locally compact classical principal G-bundles and are compatible with θ-deformation; in particular, they cover the θ-deformed quaternionic Hopf fibration C∞(S7 θ ) ← C∞(S4 θ ) as a noncommutative principal SU(2)-bundle. | |
| dc.description.copyright | © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021 This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. | |
| dc.identifier.issn | 1432-0916 | |
| dc.identifier.issn | 0010-3616 | |
| dc.identifier.uri | https://unbscholar.lib.unb.ca/handle/1882/37558 | |
| dc.language.iso | en | |
| dc.publisher | Springer | |
| dc.relation.hasversion | https://doi.org/10.1007/s00220-021-04187-8 | |
| dc.rights | http://purl.org/coar/access_right/c_abf2 | |
| dc.subject.discipline | Mathematics and Statistics | |
| dc.title | Gauge theory on noncommutative Riemannian principal bundles | |
| dc.type | journal article | |
| oaire.citation.endPage | 198 | |
| oaire.citation.startPage | 107 | |
| oaire.citation.title | Communications in Mathematical Physics | |
| oaire.citation.volume | 388 | |
| oaire.license.condition | other | |
| oaire.version | http://purl.org/coar/version/c_ab4af688f83e57aa |