Past exam of the mathematics course of the University of Cambridge / 2002 / iii / Paper 68 / 1 / c / Solution

Unbroken extended supersymmetry obstructs the observed chiral matter structure. In four dimensions, the matter hypermultiplets of $\mathcal{N}\ge 2$ theories contain conjugate gauge group representations, so their fermions are vectorlike rather than the chiral Weyl fermions of the Standard Model. Extended supersymmetry also relates interactions more strongly, restricting independent Yukawa couplings and superpotentials. It can occur at higher energies and break to $\mathcal{N}=1$ or to no supersymmetry; the objection is to its unbroken realization in an ordinary low-energy chiral particle theory.