  Supersymmetry is a powerful concept in quantum many-body physics. It helps to
illuminate ground state properties of complex quantum systems and gives
relations between correlation functions. In this work, we show that the
Sachdev-Ye-Kitaev model, in its simplest form of Majorana fermions with random
four-body interactions, is supersymmetric. In contrast to existing explicitly
supersymmetric extensions of the model, the supersymmetry we find requires no
relations between couplings. The type of supersymmetry and the structure of the
supercharges are entirely set by the number of interacting Majorana modes, and
are thus fundamentally linked to the model's Altland-Zirnbauer classification.
The supersymmetry we uncover has a natural interpretation in terms of a
one-dimensional topological phase supporting Sachdev-Ye-Kitaev boundary
physics, and has consequences away from the ground state, including in $q$-body
dynamical correlation functions.
