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This article is cited in 4 scientific papers (total in 4 papers)
Quasicomplex $\mathcal{N}=2$, $d=1$ Supersymmetric Sigma Models
Evgeny A. Ivanova, Andrei V. Smilgab a Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna, Russia
b SUBATECH, Université de Nantes, 4 rue Alfred Kastler, BP 20722, Nantes 44307, France
Abstract:
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.
Received: June 30, 2013; in final form November 13, 2013; Published online November 18, 2013
Citation:
Evgeny A. Ivanov, Andrei V. Smilga, “Quasicomplex $\mathcal{N}=2$, $d=1$ Supersymmetric Sigma Models”, SIGMA, 9 (2013), 069, 17 pp.
Linking options:
https://www.mathnet.ru/eng/sigma852 https://www.mathnet.ru/eng/sigma/v9/p69
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