全纯超曲线与超对称西格玛模型
Holomorphic Supercurves and Supersymmetric Sigma Models
摘要：
我们引入一个自然的推广全纯曲线的超流形的态射，称为全纯超曲线。更确切地说，超曲线是从黎曼曲面到普通几乎复流形的态射，黎曼曲面被赋予由全纯线丛诱导的超流形的结构。它们被称为全纯的，如果广义柯西-黎曼条件得到满足。通过作用恒等式证明了全纯超曲线是超对称作用泛函的特殊极值。
英文摘要：
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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