Abstract
We investigate the role of locally product structures in the formulation of N = 1 and N = 2 supersymmetric nonlinear σ-models in a superspace with signature (+, −, −, +). The geometric properties of the target manifolds are completely determined by the physical requirements of having chirality preserving superfields' transformations and an action that is a superspace integral of a scalar function of those superfields. As a result we obtain the N = 1 manifold presenting a locally product structure while the N = 2 manifold admits a set of tangent space automorphisms isomorphic to the split-quaternionic algebra.
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Carvalho, M., Helayël-Neto, J.A. & De Oliveira, M.W. Locally Product Structures and Supersymmetry. Letters in Mathematical Physics 64, 93–104 (2003). https://doi.org/10.1023/A:1025725618916
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DOI: https://doi.org/10.1023/A:1025725618916