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Wavefront sets and polarizations on supermanifolds

Academic Article
Publication Date:
2017
abstract:
In this paper, we develop the foundation 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
Iris type:
1.1 Articolo in rivista
Keywords:
supermanifolds, wavefront set, supersymmetric field theories
List of contributors:
Dappiaggi, Claudio; Gimperlein, Heiko; Murro, Simone; Schenkel, Alexander
Authors of the University:
DAPPIAGGI CLAUDIO
Handle:
https://iris.unipv.it/handle/11571/1174323
Published in:
JOURNAL OF MATHEMATICAL PHYSICS
Journal
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