Curvature on determinant bundles and first Chern forms

dc.creatorPaycha, Sylvie
dc.creatorRosenberg, Steven
dc.date2000-09-18
dc.date.accessioned2026-07-07T04:37:28Z
dc.date.available2026-07-07T04:37:28Z
dc.descriptionThe 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.identifierhttps://arxiv.org/abs/math/0009172
dc.identifierhttp://arxiv.org/abs/math/0009172
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/59959
dc.subjectDifferential Geometry
dc.subjectMathematical Physics
dc.titleCurvature on determinant bundles and first Chern forms
dc.typetext

Files

Collections