Wavefront sets and polarizations on supermanifolds
Abstract
In this paper we develop the foundations for microlocal analysis on supermanifolds. Making use of pseudodifferential operators on supermanifolds as introduced by Rempel and Schmitt, we define a suitable notion of super wavefront set for superdistributions which generalizes Dencker's polarization sets for vector-valued distributions to supergeometry. In particular, our super wavefront sets detect polarization information of the singularities of superdistributions. We prove a refined pullback theorem for superdistributions along supermanifold morphisms, which as a special case establishes criteria when two superdistributions may be multiplied. As an application of our framework, we study the singularities of distributional solutions of a supersymmetric field theory.
Cite
@article{arxiv.1512.07823,
title = {Wavefront sets and polarizations on supermanifolds},
author = {Claudio Dappiaggi and Heiko Gimperlein and Simone Murro and Alexander Schenkel},
journal= {arXiv preprint arXiv:1512.07823},
year = {2017}
}
Comments
26 pages, typos corrected, final version published in Journal of Mathematical Physics