1102.4920 (Josua Groeger)

Holomorphic Supercurves and Supersymmetric Sigma Models    [PDF]

Josua Groeger

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.

View original: http://arxiv.org/abs/1102.4920