6533b7d9fe1ef96bd126cbf8
RESEARCH PRODUCT
Quillen superconnections and connections on supermanifolds
José V. BeltránJosé A. VallejoJuan Monterdesubject
Mathematics - Differential GeometryHigh Energy Physics - TheoryChern classGeneral Physics and AstronomyVector bundleFOS: Physical sciences53C07 58C50 81T13Mathematical Physics (math-ph)Mathematics::Algebraic TopologyAlgebraHigh Energy Physics::TheoryDifferential Geometry (math.DG)High Energy Physics - Theory (hep-th)Mathematics::K-Theory and HomologyBundleSupermanifoldFOS: MathematicsGeometry and TopologyMathematics::Differential GeometryParametrizationMathematics::Symplectic GeometryMathematical PhysicsMathematicsdescription
Given a supervector bundle $E = E_0\oplus E_1 \to M$, we exhibit a parametrization of Quillen superconnections on $E$ by graded connections on the Cartan-Koszul supermanifold $(M;\Omega (M))$. The relation between the curvatures of both kind of connections, and their associated Chern classes, is discussed in detail. In particular, we find that Chern classes for graded vector bundles on split supermanifolds can be computed through the associated Quillen superconnections.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2013-05-16 |