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Super Riemann Surfaces and the Super Conformal Action Functional

In: Quantum Mathematical Physics

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  • Enno Keßler

    (Max-Planck-Institut für Mathematik in den Naturwissenschaften)

Abstract

Riemann surfaces are two-dimensional manifolds with a conformal class of metrics. It is well known that the harmonic action functional and harmonic maps are tools to study the moduli space of Riemann surfaces. Super Riemann surfaces are an analogue of Riemann surfaces in the world of super geometry. After a short introduction to super differential geometry we will compare Riemann surfaces and super Riemann surfaces. We will see that super Riemann surfaces can be viewed as Riemann surfaces with an additional field, the gravitino. An extension of the harmonic action functional to super Riemann surfaces is presented and applications to the moduli space of super Riemann surfaces are considered.

Suggested Citation

  • Enno Keßler, 2016. "Super Riemann Surfaces and the Super Conformal Action Functional," Springer Books, in: Felix Finster & Johannes Kleiner & Christian Röken & Jürgen Tolksdorf (ed.), Quantum Mathematical Physics, edition 1, pages 401-419, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-26902-3_17
    DOI: 10.1007/978-3-319-26902-3_17
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