Super $J$-holomorphic Curves: Construction of the Moduli Space

Abstract

Let $M$ be a super Riemann surface with holomorphic distribution $\mathcal{D}$ and $N$ a symplectic manifold with compatible almost complex structure $J$. We call a map $\Phi :M\to N$ a super $J$-holomorphic curve if its differential maps the almost complex structure on $\mathcal{D}$ to $J$. Such a super $J$-holomorphic curve is a critical point for the superconformal action and satisfies a super differential equation of first order. Using component fields of this super differential equation and a transversality argument we construct the moduli space of super $J$-holomorphic curves as a smooth subsupermanifold of the space of maps $M\to N$.

v2: added a section on surjectivity of the Dirac operator and examples; fixed dimension formula and typos

References in corpus (3)

• Super Riemann surfaces, metrics, and gravitinos
• Global Analytic Approach to Super Teichmueller Spaces
• A Supermanifold structure on Spaces of Morphisms between Supermanifolds

Cited by in corpus (1)

• Super quantum cohomology I: Super stable maps of genus zero with Neveu-Schwarz punctures