Extension of Conformal (Super)Symmetry using Heisenberg and Parabose operators

TL;DR

This paper explores extending conformal and superconformal symmetry using Heisenberg and parabose operators, proposing a simple mathematical framework that relaxes traditional symmetry constraints and discusses implications for theories with broken symmetries.

Contribution

It introduces a novel extension of conformal superalgebra via nonzero anticommutators, broadening the mathematical structure of conformal symmetries using Heisenberg and parabose operators.

Findings

Extended conformal superalgebra from standard algebra

Allows nonzero anticommutators in supersymmetry

Discusses implications for broken symmetry theories

Abstract

In this paper we investigate a particular possibility to extend C(1,3) conformal symmetry using Heisenberg operators, and a related possibility to extend conformal supersymmetry using parabose operators. The symmetry proposed is of a simple mathematical form, as is the form of necessary symmetry breaking that reduces it to the conformal (super)symmetry. It turns out that this extension of conformal superalgebra can be obtained from standard non-extended conformal superalgebra by allowing anticommutators $\{Q_\eta, Q_\xi\}$ and $\{\bar Q_{\dot \eta}, \bar Q_{\dot \xi}\}$ to be nonzero operators and then by closing the algebra. In regard of the famous Coleman and Mandula theorem (and related Haag-Lopuszanski-Sohnius theorem), the higher symmetries that we consider do not satisfy the requirement for finite number of particles with masses below any given constant. However, we argue that in the context of theories with broken symmetries, this constraint may be unnecessarily strong.