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Quasicomplex $\mathcal{N}=2$, $d=1$ Supersymmetric Sigma Models
Symmetry, integrability and geometry: methods and applications, Tome 9 (2013) Cet article a éte moissonné depuis la source Math-Net.Ru

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We derive and discuss a new type of $\mathcal{N}=2$ supersymmetric quantum mechanical sigma models which appear when the superfield action of the ($\mathbf{1, 2, 1}$) multiplets is modified by adding an imaginary antisymmetric tensor to the target space metric, thus completing the latter to a non-symmetric Hermitian metric. These models are not equivalent to the standard de Rham sigma models, but are related to them through a certain special similarity transformation of the supercharges. On the other hand, they can be obtained by a Hamiltonian reduction from the complex supersymmetric $\mathcal{N}=2$ sigma models built on the multiplets ($\mathbf{2, 2, 0}$) and describing the Dolbeault complex on the manifolds with proper isometries. We study in detail the extremal two-dimensional case, when the target space metric is defined solely by the antisymmetric tensor, and show that the corresponding quantum systems reveal a hidden $\mathcal{N}=4$ supersymmetry.
Keywords: supersymmetry; geometry; superfield. 
@article{SIGMA_2013_9_a68,
     author = {Evgeny A. Ivanov and Andrei V. Smilga},
     title = {Quasicomplex $\mathcal{N}=2$, $d=1$ {Supersymmetric} {Sigma} {Models}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2013},
     volume = {9},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2013_9_a68/}
}
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Evgeny A. Ivanov; Andrei V. Smilga. Quasicomplex $\mathcal{N}=2$, $d=1$ Supersymmetric Sigma Models. Symmetry, integrability and geometry: methods and applications, Tome 9 (2013). http://geodesic.mathdoc.fr/item/SIGMA_2013_9_a68/

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