Super \(J\)-holomorphic curves: construction of the moduli space. (English) Zbl 1496.32043
Summary: 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 \(\Phi :M\rightarrow N\) 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 \(M\rightarrow N\).
MSC:
| 32Q65 | Pseudoholomorphic curves |
| 32Q60 | Almost complex manifolds |
| 58C50 | Analysis on supermanifolds or graded manifolds |
| 58D27 | Moduli problems for differential geometric structures |
| 53D45 | Gromov-Witten invariants, quantum cohomology, Frobenius manifolds |
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
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