Abstract
We construct \( \mathcal{N}=2 \) supersymmetric nonlinear sigma models on the cotangent bundles over the non-compact exceptional Hermitian symmetric spaces \( \mathrm{\mathcal{M}}={E}_{6\left(-14\right)}/\mathrm{SO}(10)\times \mathrm{U}(1) \) and E7(−25)/E6 × U(1). In order to construct them we use the projective superspace formalism which is an \( \mathcal{N}=2 \) off-shell superfield formulation in four-dimensional space-time. This formalism allows us to obtain the explicit expression of \( \mathcal{N}=2 \) supersymmetric nonlinear sigma models on the cotangent bundles over any Hermitian symmetric spaces in terms of the \( \mathcal{N}=1 \) superfields, once the Kähler potentials of the base manifolds are obtained. We derive the \( \mathcal{N}=1 \) supersymmetric nonlinear sigma models on the Kähler manifolds \( \mathrm{\mathcal{M}} \). Then we extend them into the \( \mathcal{N}=2 \) supersymmetric models with the use of the result in arXiv:1211.1537 developed in the projective superspace formalism. The resultant models are the \( \mathcal{N}=2 \) supersymmetric nonlinear sigma models on the cotangent bundles over the Hermitian symmetric spaces \( \mathrm{\mathcal{M}} \). In this work we complete constructing the cotangent bundles over all the compact and non-compact Hermitian symmetric spaces.
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Arai, M., Baba, K. Supersymmetry and cotangent bundle over non-compact exceptional Hermitian symmetric space. J. High Energ. Phys. 2015, 169 (2015). https://doi.org/10.1007/JHEP07(2015)169
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DOI: https://doi.org/10.1007/JHEP07(2015)169