  The supersymmetric Lee-Yang model is arguably the simplest interacting
supersymmetric field theory in two dimensions, albeit non-unitary. A natural
question is if there is an analogue of supersymmetric Lee-Yang fixed point in
higher dimensions. The absence of any $\mathbb{Z}_2$ symmetry (except for
fermion numbers) makes it impossible to approach it by using perturbative
$\epsilon$ expansions. We find that the truncated conformal bootstrap suggests
that candidate fixed points obtained by the dimensional continuation from two
dimensions annihilate below three dimensions, implying that there is no
supersymmetric Lee-Yang fixed point in three dimensions. We conjecture that the
corresponding phase transition, if any, will be the first order transition.
