Automorphism groups of N=2 superconformal super-Riemann spheres

TL;DR

This paper determines the automorphism groups of N=2 superconformal super-Riemann spheres with genus-zero bodies and explores their Lie structures, extending results to N=1 superanalytic structures.

Contribution

It explicitly characterizes the automorphism groups of N=2 superconformal super-Riemann spheres and analyzes their Lie algebra structures, extending findings to N=1 superanalytic surfaces.

Findings

Automorphism groups are explicitly determined for N=2 superconformal super-Riemann spheres.

Lie structures of these automorphism groups are analyzed.

Results extend to N=1 superanalytic super-Riemann surfaces.

Abstract

In previous work, the author proved that there is a countably infinite family of N=2 superconformal equivalence classes of DeWitt N=2 superconformal super-Riemann surfaces with closed, genus-zero body. In this paper, we determine the automorphism groups for these N=2 superconformal super-Riemann surfaces, and analyze the Lie structure of these groups. Under the correspondence between N=2 superconformal and N=1 superanalytic structures, the results extend to the determination of automorphism groups of N=1 superanalytic DeWitt super-Riemann surfaces with closed, genus-zero body.