Given a WZW term (a differential cocycle) on some , and given a -manifold , a definite globalization of over is a WZW term on which is suitably locally equivalent to . In particular the curvature form of is a definite form on , definite on the curvature form of the local model .
Hence a definite globalization of a WZW term may be thought of as a higher prequantization of a definite form.
Definite gobalizations of WZW terms induce definite parameterizations, namely parameterization of the restriction of to the infinitesimal disk in , over the infinitesimal disk bundle of . These in turn correspond to G-structures for the homotopy stabilizer group of .
By the Darboux theorem for line bundles, every prequantization of a symplectic manifold is automatically a definite globalization of some fixed pre-quantization of .
The equations of motion of supergravity theories typically imply that the WZW curvatures of the relevant super p-brane sigma models on super Minkowski spacetime extend as definite forms over the super-spacetime. Hence the full WZW term defining the super p-brane sigma model needs to be a definite globalization over super-spacetime of the local model over super-Minkowski spacetime.
Last revised on July 31, 2017 at 08:36:26. See the history of this page for a list of all contributions to it.