Decorated Super-Teichm\"uller Space
R.C. Penner, Anton M. Zeitlin

TL;DR
This paper develops a super-analogue of decorated Teichmüller space by introducing new coordinates and transformations in super Minkowski space, extending classical structures to include fermionic invariants.
Contribution
It introduces coordinates for a super Teichmüller space, extending lambda lengths with fermionic invariants, and establishes super Ptolemy transformations and a super Weil-Petersson form.
Findings
Defined super lambda length coordinates
Established super Ptolemy transformations
Constructed a super Weil-Petersson form
Abstract
We introduce coordinates for a principal bundle over the super Teichmueller space of a surface with punctures that extend the lambda length coordinates on the decorated bundle over the usual Teichmueller space . In effect, the action of a Fuchsian subgroup of on Minkowski space is replaced by the action of a super Fuchsian subgroup of on the super Minkowski space , where denotes the orthosymplectic Lie supergroup, and the lambda lengths are extended by fermionic invariants of suitable triples of isotropic vectors in . As in the bosonic case, there is the analogue of the Ptolemy transformation now on both even and odd coordinates as well as an invariant even two-form on generalizing the…
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