Moduli of super Riemann surfaces

We generalize the result of [13] to give an expression for the super Mumford form µ on the moduli spaces of super Riemann surfaces with Ramond and Neveu-Schwarz punctures. In the Ramond case we take the number of punctures to be large compared to the genus. We consider for the case of Neveu-Schwarz punctures the super Mumford form over the component of the moduli space corresponding to an odd spin structure. The super Mumford form µ can be used to create a measure whose integral computes scattering amplitudes of superstring theory. We express µ in terms of local bases of H 0 (X, ω j ) for ω the Berezinian line bundle of a family of super Riemann surfaces.

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“…In superstring theory, Friedan in [Fri86] identified the super Riemann surface as the wordsheet to be swept out by the superstrings in superspacetimes. Once clearly defined, further work on the mathematical properties of super Riemann surfaces and their moduli were undertaken, e.g., in [CR88,DRS90,LR88,FR90b]; in addition to some extensions of super Riemann surfaces to Riemann surfaces with higher degrees of supersymmetry in [Coh87,FR90a]. More recently, Donagi and Witten in [DW15,DW14] have revived interest in this topic with some landmark results on the geometry of their moduli.…”

Section: Algebraic Deformations and Supermodulimentioning

confidence: 99%

On the problem of splitting deformations of super Riemann surfaces

Bettadapura¹

2018

Lett Math Phys

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By analytic deformations of complex structures, we mean perturbations of the Dolbeault operator. By algebraic deformations of complex structures, we mean deformations of holomorphic glueing data. For complex manifolds there is, infinitesimally, a correspondence between these two types deformations. In this article we argue that an analogous correspondence holds between the analytic and algebraic deformations of a super Riemann surface.

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Moduli of super Riemann surfaces

Abstract: The basic properties of super Riemann surfaces are presented, and their supermoduli spaces are constructed, in a manner suitable for the application of algebro-geometric techniques to string theory.

Cited by 69 publications

References 11 publications

The super complex Frobenius theorem

The super complex Frobenius theorem

On the super Mumford form in the presence of Ramond and Neveu–Schwarz punctures

On the problem of splitting deformations of super Riemann surfaces

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