Low dimensional supersymmetries in SUSY Chern–Simons systems and geometrical implications

Abstract

We study in detail the underlying graded geometric structure of abelian [Formula: see text] supersymmetric Chern–Simons theory in (2 + 1)-dimensions. This structure is an attribute of the hidden unbroken one-dimensional [Formula: see text] supersymmetries that the system also possesses. We establish the result that the geometric structures corresponding to the bosonic and to the fermionic sectors are equivalent fiber bundles over the (2 + 1)-dimensional manifold. Moreover, we find a geometrical answer to the question why some and not all of the fermionic sections are related to a [Formula: see text] supersymmetric algebra. Our findings are useful for the quantum theory of Chern–Simons vortices.