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arXiv · 1907.07256

The Super Mumford Form in the Presence of Ramond and Neveu-Schwarz Punctures

Daniel J. Diroff
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Abstract

We generalize the result of Voronov (1988) 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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Daniel J. Diroff. 2019-07-16. The Super Mumford Form in the Presence of Ramond and Neveu-Schwarz Punctures. https://arxiv.org/abs/1907.07256

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