Polar supermultiplets, hermitian symmetric spaces and hyperkähler metrics

We address the construction of four-dimensional {N} = 2 supersymmetric nonlinear sigma models on tangent bundles of arbitrary Hermitian symmetric spaces starting from projective superspace. Using a systematic way of solving the (infinite number of) auxiliary field equations along with the requirement of supersymmetry, we are able to derive a closed form for the Lagrangian on the tangent bundle and to dualize it to give the hyperkähler potential on the cotangent bundle. As an application, the case of the exceptional symmetric space E6/SO(10) × U(1) is explicitly worked out for the first time.