Quasicomplex N =2, d =1 Supersymmetric Sigma Models

[摘要] We derive and discuss a new type of N =2 supersymmetric quantum mechanical sigma models which appear when the superfield action of the ( 1 , 2 , 1 ) multiplets is modified by adding an imaginary antisymmetric tensor to the target space metric, thus completing the latter to a non-symmetric Hermitian metric. These models are not equivalent to the standard de Rham sigma models, but are related to them through a certain special similarity transformation of the supercharges. On the other hand, they can be obtained by a Hamiltonian reduction from the complex supersymmetric N =2 sigma models built on the multiplets ( 2 , 2 , 0 ) and describing the Dolbeault complex on the manifolds with proper isometries. We study in detail the extremal two-dimensional case, when the target space metric is defined solely by the antisymmetric tensor, and show that the corresponding quantum systems reveal a hidden N =4 supersymmetry.

[关键词] supersymmetry;geometry;superfield