Cotangent bundles over all the Hermitian symmetric spaces

23rd International Conference on Integrable Systems and Quantum Symmetries

Arai, Masato^1 ; Baba, Kurando^2

Faculty of Science, Yamagata University, Kojirakawa-machi 1-4-12, Yamagata, Yamagata

990-8560, Japan^1

Department of General Education, Fukushima National College of Technology, Fukushima

970-8034, Japan^2

关键词: Four-dimensional space;    General formulas;    Hermitian symmetric spaces;    Nonlinear sigma model;    Superspace formalism;    Supersymmetric models;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/670/1/012005/pdf
DOI  :  10.1088/1742-6596/670/1/012005

来源: IOP

【 摘 要 】

We construct the N = 2 supersymmetric nonlinear sigma models on the cotangent bundles over all the compact and non-compact Hermitian symmetric spaces. 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. Starting with N = 1 supersymmetric Kahler nonlinear sigma models on the Hermitian symmetric spaces, we extend them into the N = 2 supersymmetric models by using the projective superspace formalism and derive the general formula for the cotangent bundles over all the compact and non-compact Hermitian symmetric spaces. We apply to the formula for the non-compact Hermitian symmetric space E7/E6× U(1)1.