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We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
The functional of super Riemann surfaces – a “semi-classical” survey
Enno Keßler and Jürgen TolksdorfAbstract
This article provides a brief discussion of the functional of super Riemann surfaces from the point of view of classical (i.e. not “super-”) differential geometry. The discussion is based on symmetry considerations and aims to clarify the “borderline” between classical and super differential geometry with respect to the distinguished functional that generalizes the action of harmonic maps and is expected to play a basic role in the discussion of “super Teichmüller space”. The discussion is also motivated by the fact that a geometrical understanding of the functional of super Riemann surfaces from the point of view of super geometry seems to provide serious issues to treat the functional analytically.
- Received:
- 01.12.15
- Published:
- 01.12.15
- MSC Codes:
- 58A50, 14H55, 32G15
- PACS:
- 02.40.Ky, 03.50.Kk, 03.65.Sq, 11.30.Pb, 12.60.Jv
- Keywords:
- clifford modules, Dirac operators, Torsion, Non-linear Sigma-models, Super Riemann surfaces, supersymmetry