Moduli Space, of SRS

Two N Super riemann surfaces P ₁ = Λ ^NS/Γ₁ and P ₂ = Λ ^NS/Γ₂ are called isomorphic if the N super Fuchsian groups Γ₁ and Γ₂ are conjugate in Aut(Λ ^NS). The set of isomorphism classes of Super riemann surfaces is called the moduli space of Super riemann surfaces . The topological type of Super riemann surfaces is defined by the topological types of its Arf functions (see section Super riemann surfaces and Arf functions for details). The set of all Super riemann surfaces of any topological type t has a natural structure of a connected super manifold M ^t [1 2 3].

If t = (g, δ, k _α, m _α) is a topological type of N = 1 Super riemann surfaces that M ^t ≅ ℝ^{(6g+3k+2m−6|4g+2k +2m−4)}/ Mod _t , where Mod _t is a discrete group (the definition of ℝ^(n|ℓ) see in the section super Fuchsian group ).

If t = (g, δ, k _α, m _α) is a topological type of N = 2 nontwisted Super riemann surfaces , then M ^t ≅ ℝ^{(8g+4k+3m−b|8g+4k+4m−8)}/ Mod _t *, where b = 6 if k = m = 0, b = 7 otherwise and Mod* _t is a discrete...