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arXiv · 1512.07823

Wavefront sets and polarizations on supermanifolds

Claudio Dappiaggi·Heiko Gimperlein·Simone Murro·Alexander Schenkel
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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.

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Claudio Dappiaggi, Heiko Gimperlein, Simone Murro, Alexander Schenkel. 2017-02-15. Wavefront sets and polarizations on supermanifolds. https://doi.org/10.1063/1.4975213

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