Supersymmetry and Cotangent Bundle over Non-compact Exceptional Hermitian Symmetric Space

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We construct N=2 supersymmetric nonlinear sigma models on the cotangent bundles over the non-compact exceptional Hermitian symmetric spaces M=E₆₍₋₁₄₎/SO(10)xU(1) and E₇₍₋₂₅₎/E₆xU(1). In order to construct them we use the projective superspace formalism which is an N=2 off-shell superfield formulation in four-dimensional space-time. This formalism allows us to obtain the explicit expression of N=2 supersymmetric nonlinear sigma models on the cotangent bundles over any Hermitian symmetric spaces in terms of the N=1 superfields, once the Kahler potentials of the base manifolds are obtained. We derive the N=1 supersymmetric nonlinear sigma models on the Kahler manifolds M. Then we extend them into the N=2 supersymmetric models with the use of the result in arXiv:1211.1537 developed in the projective superspace formalism. The resultant models are the N=2 supersymmetric nonlinear sigma models on the cotangent bundles over the Hermitian symmetric spaces M. In this work we complete constructing the cotangent bundles over all the compact and non-compact Hermitian symmetric spaces.