  We investigate a class of supersymmetric quantum mechanical theories (with
two supercharges) having tensor-valued degrees of freedom which are dominated
by melon diagrams in the large $N$ limit. One motivation was to examine the
interplay between supersymmetry and melonic dominance and potential
implications for building toy models of holography. We find a definite tension
between supersymmetry (with dynamical bosons) and melonic dominance in this
class of systems. More specifically, our theories attain a low energy
non-supersymmetric conformal fixed point. The origin of supersymmetry breaking
lies in the need to regularize bosonic and fermionic degrees of freedom
independently. We investigate various aspects of the low energy spectrum and
also comment on related examples with different numbers of supercharges. Along
the way we also derive some technical results for $SL(2,{\mathbb R})$
wavefunctions for fermionic excitations.
