First-order supersymmetric sigma models and target space geometry -: art. no. 144

We study the conditions under which N = ( 1, 1) generalized sigma models support an extension to N = ( 2, 2). The enhanced supersymmetry is related to the target space complex geometry. Concentrating on a simple situation, related to Poisson sigma models we develop a language that may help us analyze more complicated models in the future. In particular, we uncover a geometrical framework which contains generalized complex geometry as a special case.