Low Dimensional Supersymmetries in SUSY Chern-Simons Systems and Geometrical Implications

TL;DR

This paper explores the geometric structures underlying N=2 supersymmetric Chern-Simons theory in 2+1 dimensions, revealing equivalences in fiber bundles and explaining the selective supersymmetry of fermionic sections, with implications for quantum vortex analysis.

Contribution

It uncovers the graded geometric structure of the theory, showing the equivalence of bosonic and fermionic fiber bundles and explaining the partial supersymmetry of fermionic sections.

Findings

Bosonic and fermionic sectors form equivalent fiber bundles.

Only some fermionic sections relate to N=2 supersymmetry.

Results aid the quantum analysis of Chern-Simons vortices.

Abstract

We study in detail the underlying graded geometric structure of abelian N=2 supersymmetric Chern-Simons theory in $(2+1)$-dimensions. This structure is an attribute of the hidden unbroken one dimensional N=2 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 fibre 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 N=2 supersymmetric algebra. Our findings are useful for the quantum theory of Chern-Simons vortices.