Supersymmetry does not imply mass degeneracy
It is commonly believed that unbroken supersymmetry (SUSY) implies that all members of a supermultiplet have the same mass. We demonstrate that this is not true, by exhibiting a simple counterexample. We employ the formalism of homeotic fermions, in a simple model where CPT conjugate fermions have different masses. This model can be supersymmetrized to a hypermultiplet of fields which form a representation of the conventional N=2 SUSY algebra. Nevertheless, CPT conjugate states in this hypermultiplet have different masses. These surprising results do not violate either the CPT theorem or the Haag¿Lopuszański¿Sohnius theorem.
Barenboim Szuchman, Gabriela Alejandra Lykken, Joseph 2004 Supersymmetry does not imply mass degeneracy Physics Letters B 583 3¿4 304 308