Generalized Kahler geometry and manifest N = (2,2) supersymmetric nonlinear sigma-models -: art. no. 067

Generalized complex geometry is a new mathematical framework that is useful for describing the target space of N = ( 2; 2) nonlinear sigma-models. The most direct relation is obtained at the N = ( 1; 1) level when the sigma model is formulated with an additional auxiliary spinorial field. We revive a formulation in terms of N = ( 2; 2) semi( anti) chiral multiplets where such auxiliary fields are naturally present. The underlying generalized complex structures are shown to commute ( unlike the corresponding ordinary complex structures) and describe a Generalized Kahler geometry. The metric, B-field and generalized complex structures are all determined in terms of a potential K.