  We study a quantum mechanical model proposed by Sachdev, Ye and Kitaev. The
model consists of $N$ Majorana fermions with random interactions of a few
fermions at a time. It it tractable in the large $N$ limit, where the classical
variable is a bilocal fermion bilinear. The model becomes strongly interacting
at low energies where it develops an emergent conformal symmetry. We study two
and four point functions of the fundamental fermions. This provides the
spectrum of physical excitations for the bilocal field.
  The emergent conformal symmetry is a reparametrization symmetry, which is
spontaneously broken to $SL(2,R)$, leading to zero modes. These zero modes are
lifted by a small residual explicit breaking, which produces an enhanced
contribution to the four point function. This contribution displays a maximal
Lyapunov exponent in the chaos region (out of time ordered correlator). We
expect these features to be universal properties of large $N$ quantum mechanics
systems with emergent reparametrization symmetry.
  This article is largely based on talks given by Kitaev \cite{KitaevTalks},
which motivated us to work out the details of the ideas described there.
