On Ramond Decorations

TL;DR

This paper studies the structure of super Teichmüller space with Ramond punctures, imposing constraints on monodromies to align odd dimensions with super Riemann surface moduli.

Contribution

It introduces specific constraints on monodromies around Ramond punctures to match the odd dimensions of super Teichmüller space with super Riemann surface moduli.

Findings

Monodromy around Ramond punctures must be a true parabolic element.

Constraints reduce odd dimension to match super Riemann surface moduli.

Provides a uniformization perspective for super Teichmüller space.

Abstract

We impose constraints on the odd coordinates of super Teichm\"uller space in the uniformization picture for the monodromies around Ramond punctures, thus reducing the overall odd dimension to be compatible with that of the moduli spaces of super Riemann surfaces. Namely, the monodromy of a puncture must be a true parabolic element of the canonical subgroup $PSL(2,\mathbb{R})$.