Wavefront sets and polarizations on supermanifolds

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