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Holomorphic supercurves and supersymmetric sigma models. (English) Zbl 1273.81148
Summary: 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.{
©2011 American Institute of Physics}

81T10 Model quantum field theories
81T20 Quantum field theory on curved space or space-time backgrounds
81T60 Supersymmetric field theories in quantum mechanics
58C50 Analysis on supermanifolds or graded manifolds
14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
32Q05 Negative curvature complex manifolds
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