Parabose algebra as generalized conformal supersymmetry

TL;DR

This paper explores parabose N=4 algebra as an extension of conformal supersymmetry, suggesting that relaxing Lorentz covariance allows for a broader symmetry structure that can be reduced to observable symmetries.

Contribution

It introduces a generalized conformal supersymmetry based on parabose algebra, expanding the understanding of symmetry structures beyond traditional frameworks.

Findings

Parabose N=4 algebra extends conformal supersymmetry in four dimensions.

Relaxing Lorentz covariance reveals a larger symmetry containing two SU(2) groups.

Breaking one SU(2) to U(1) reduces symmetry to observable form.

Abstract

The form of realistic space-time supersymmetry is fixed, by Haag-Lopuszanski-Sohnius theorem, either to the familiar form of Poincare supersymmetry or, in massless case, to that of conformal supersymmetry. We question necessity for such strict restriction in the context of theories with broken symmetries. In particular, we consider parabose N=4 algebra as an extension of conformal supersymmetry in four dimensions (coinciding with the, so called, generalized conformal supersymmetry). We show that sacrificing of manifest Lorentz covariance leads to interpretation of the generalized conformal supersymmetry as symmetry that contains, on equal footing, two "rotation" groups. It is possible to reduce this large symmetry down to observable one by simply breaking one of these two SU(2) isomorphic groups down to its U(1) subgroup.