Super Riemann surfaces, metrics, and gravitinos

Jürgen Jost, Enno Keßler, and Jürgen Tolksdorf

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Submission date: 18. Dec. 2014 (revised version: December 2015)
Pages: 22
published in: Advances in theoretical and mathematical physics, 21 (2017) 5, p. 1161-1187 
DOI number (of the published article): 10.4310/ATMP.2017.v21.n5.a2
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Abstract:
The underlying even manifold of a super Riemann surface is a Riemann surface with a spinor valued differential form called gravitino. Consequently infinitesimal deformations of super Riemann surfaces are certain infinitesimal deformations of the Riemann surface and the gravitino. Furthermore the action functional of non-linear super symmetric sigma models, the action functional underlying string theory, can be obtained from a geometric action functional on super Riemann surfaces. All invariances of the super symmetric action functional are explained in super geometric terms and the action functional is a functional on the moduli space of super Riemann surfaces.