Hidden supersymmetry and quadratic deformations of the space-time conformal superalgebra

TL;DR

This paper investigates quadratic deformations of N=1 conformal supersymmetry, revealing that massless positive energy representations form zero-step modules where supersymmetry is unbroken and superpartners are absent.

Contribution

It characterizes zero-step modules in quadratic superalgebras for N=1 conformal supersymmetry and shows massless representations form such modules with unbroken quadratic supersymmetry.

Findings

Massless positive energy representations are zero-step modules.

Quadratic supersymmetry is unbroken for these representations.

Superpartners do not exist in these zero-step modules.

Abstract

We analyze the structure of the family of quadratic superalgebras, introduced in J Phys A 44(23):235205 (2011), for the quadatic deformations of $N = 1$ space-time conformal supersymmetry. We characterize in particular the `zero-step' modules for this case. In such modules, the odd generators vanish identically, and the quadratic superalgebra is realized on a single irreducible representation of the even subalgebra (which is a Lie algebra). In the case under study, the quadratic deformations of $N = 1$ space-time conformal supersymmetry, it is shown that each massless positive energy unitary irreducible representation (in the standard classification of Mack), forms such a zero-step module, for an appropriate parameter choice amongst the quadratic family (with vanishing central charge). For these massless particle multiplets therefore, quadratic supersymmetry is unbroken, in that the supersymmetry generators annihilate \emph{all} physical states (including the vacuum state), while at the same time, superpartners do not exist.