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arXiv · 2307.02706

Super Riemann surfaces and fatgraphs

Albert S. Schwarz·Anton M. Zeitlin
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Abstract

Our goal is to describe superconformal structures on super Riemann surfaces (SRS), based on data assigned to a fatgraph. We start from the complex structures on punctured $(1|1)$-supermanifolds, characterizing the corresponding moduli and the deformations using Strebel differentials and certain Čech cocycles for a specific covering, which we reproduce from a fatgraph data, consisting of $U(1)$-graph connection and odd parameters at the vertices. Then we consider dual $(1|1)$-supermanifolds and related superconformal structures for $N=2$ super Riemann surfaces. The superconformal structures $N=1$ SRS are computed as the fixed points of involution on supermoduli space of $N=2$ SRS.

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Albert S. Schwarz, Anton M. Zeitlin. 2023-09-23. Super Riemann surfaces and fatgraphs. https://doi.org/10.3390/universe9090384

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