Conformal supermultiplets without superpartners

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.