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Geometry of sigma -models with heterotic supersymmetry

The authors apply the method of harmonic superspace for solving locally the torsion constraints for the manifolds of (4, 0) supersymmetric sigma -models. The solution is given in terms of an unconstrained harmonic-analytic prepotential with a curved vector index. This prepotential also determines the form of the most general off-shell (4, 0) sigma -model action. The torsion-free (hyper-Kahler) case is recovered if one takes the gradient of a scalar analytic superfield as the vector potential.