Semichirals and Four Dimensional Geometry

Authors: Ulf Lindström Preprint number: UUITP-09/15 Semichiral $(2,2)$ sigma models with $4d$ target space are discussed. A novel description in $(1,1)$ superspace allows an analysis of possible extended supersymmetries. It is argued that a manifest semichiral realization of an extra supersymmetry is only possible for hyperk\"ahler target geometry.