Super J-holomorphic Curves: Construction of the Moduli Space

Enno Kessler, Artan Sheshmani, Shing-Tung Yau

Research output: Working paper/Preprint Working paperResearch

Abstract

Let M be a super Riemann surface with holomorphic distribution D and N a symplectic manifold with compatible almost complex structure J. We call a map Φ:M→N a super J-holomorphic curve if its differential maps the almost complex structure on 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→N.
Original languageEnglish
PublisherArXiv
Publication statusPublished - 13 Nov 2019

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