The functional of super Riemann surfaces – a “semi-classical” survey

Enno Keßler and Jürgen Tolksdorf

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Submission date: 01. Dec. 2015
Pages: 18
published in: Vietnam journal of mathematics, 44 (2016) 1, p. 215-229 
DOI number (of the published article): 10.1007/s10013-016-0183-1
Bibtex
with the following different title: The functional of super Riemann surfaces : a 'semi-classical' survey ; in honor of Prof. E. Zeidler's 75th birthday
MSC-Numbers: 58A50, 14H55, 32G15
PACS-Numbers: 02.40.Ky, 03.50.Kk, 03.65.Sq, 11.30.Pb, 12.60.Jv
Keywords and phrases: clifford modules, Dirac operators, Torsion, Non-linear Sigma-models, Super Riemann surfaces, supersymmetry
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Abstract:
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.