Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 9 (2013), 069, 17 pages      arXiv:1302.2902      http://dx.doi.org/10.3842/SIGMA.2013.069

Quasicomplex N=2, d=1 Supersymmetric Sigma Models

Evgeny A. Ivanov a and Andrei V. Smilga b
a) Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna, Russia
b) SUBATECH, Université de Nantes, 4 rue Alfred Kastler, BP 20722, Nantes 44307, France

Received June 30, 2013, in final form November 13, 2013; Published online November 18, 2013

Abstract
We derive and discuss a new type of N=2 supersymmetric quantum mechanical sigma models which appear when the superfield action of the (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 N=2 sigma models built on the multiplets (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 N=4 supersymmetry.

Key words: supersymmetry; geometry; superfield.

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