Wavefront sets and polarizations on supermanifolds

Claudio Dappiaggi, Heiko Gimperlein, Simone Murro, Alexander Schenkel

Research output: Contribution to journalArticle

35 Downloads (Pure)

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 languageEnglish
Article number023504
Number of pages16
JournalJournal of Mathematical Physics
Volume58
Issue number2
Early online date13 Feb 2017
DOIs
Publication statusPublished - Feb 2017

Fingerprint Dive into the research topics of 'Wavefront sets and polarizations on supermanifolds'. Together they form a unique fingerprint.

  • Cite this