Conformal supermultiplets without superpartners

TL;DR

This paper explores polynomial deformations of Lie superalgebras, revealing the existence of zero step supermultiplets that contain standard model fields without superpartners, challenging traditional supersymmetry concepts.

Contribution

It introduces quadratic and cubic deformations of superalgebras, demonstrating zero step supermultiplets for conformal groups that include standard model particles without superpartners.

Findings

Zero step supermultiplets exist for deformed superalgebras.

Standard model fields can be part of supermultiplets without superpartners.

Proposes elevating deformed superalgebras to S-matrix symmetries.

Abstract

We consider polynomial deformations of Lie superalgebras and their representations. For the class A(n-1,0) ~ sl(n/1), we identify families of superalgebras of quadratic and cubic type, consistent with Jacobi identities. For such deformed superalgebras we point out the possibility of zero step supermultiplets, carried on a single, irreducible representation of the even (Lie) subalgebra. For the conformal group SU(2,2) in 1+3-dimensional spacetime, such irreducible (unitary) representations correspond to standard conformal fields (j_1,j_2;d), where (j_1,j_2) is the spin and d the conformal dimension; in the massless class j_1 j_2=0, and d=j_1+j_2+1. We show that these repesentations are zero step supermultiplets for the superalgebra SU_(2)(2,2/1), the quadratic deformation of conformal supersymmetry SU(2,2/1). We propose to elevate SU_(2)(2,2/1) to a symmetry of the S-matrix. Under this scenario, low-energy standard model matter fields (leptons, quarks, Higgs scalars and gauge fields) descended from such conformal supermultiplets are not accompanied by superpartners.