Hyperkahler metrics building in the 1 + 3 representation

In this paper, the authors construct the HST type hyperkahler N = 2 supersymmetric nonlinear σ model. The authors show that for 4n dimensional hyperkahler manifolds, one needs in general n(n + 1)/2 scalar functions to specify the metric. The n = 1 and n = 2 are studied in detail. The SU(2) x U(1) Taub-Nut model in the HST hypermultiplet representation is discussed as an illustrating example. The corresponding Taub-Nut metric is worked out explicitly. Some general features of these models are discussed