Holomorphic Supercurves and Supersymmetric Sigma Models

Details Holomorphic Supercurves and Supersymmetric Sigma Models Holomorphic Supercurves and Supersymmetric Sigma Models

2011-02-24

arxiv.org/abs/1102.4920v1

Physics

Mathematical Physics

38 pages

Scientific paper

We introduce a natural generalisation of holomorphic curves to morphisms of supermanifolds, referred to as holomorphic supercurves. More precisely, supercurves are morphisms from a Riemann surface, endowed with the structure of a supermanifold which is induced by a holomorphic line bundle, to an ordinary almost complex manifold. They are called holomorphic if a generalised Cauchy-Riemann condition is satisfied. We show, by means of an action identity, that holomorphic supercurves are special extrema of a supersymmetric action functional.

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