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.
Original language | English |
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Article number | 023504 |
Number of pages | 16 |
Journal | Journal of Mathematical Physics |
Volume | 58 |
Issue number | 2 |
Early online date | 13 Feb 2017 |
DOIs | |
Publication status | Published - Feb 2017 |