Curvature on determinant bundles and first Chern forms
| dc.creator | Paycha, Sylvie | |
| dc.creator | Rosenberg, Steven | |
| dc.date | 2000-09-18 | |
| dc.date.accessioned | 2026-07-07T04:37:28Z | |
| dc.date.available | 2026-07-07T04:37:28Z | |
| dc.description | The Quillen-Bismut-Freed construction associates a determinant line bundle with connection to an infinite dimensional super vector bundle with a family of Dirac-type operators. We define the regularized first Chern form of the infinite dimensional bundle, and relate it to the curvature of the Bismut-Freed connection on the determinant bundle. In finite dimensions, these forms agree (up to sign), but in infinite dimensions there is a correction term, which we express in terms of Wodzicki residues. We illustrate these results with a string theory computation. There is a natural super vector bundle over the manifold of smooth almost complex structures on a Riemannian surface. The Bismut-Freed superconnection is identified with classical Teichmuller theory connections, and its curvature and regularized first Chern form are computed. | |
| dc.identifier | https://arxiv.org/abs/math/0009172 | |
| dc.identifier | http://arxiv.org/abs/math/0009172 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59959 | |
| dc.subject | Differential Geometry | |
| dc.subject | Mathematical Physics | |
| dc.title | Curvature on determinant bundles and first Chern forms | |
| dc.type | text |