  The Sachdev-Ye-Kitaev (SYK) model, a theory of N Majorana fermions with
q-body interactions, becomes in the large q limit a conformally-broken
Liouville field theory. Taking this limit preserves many interesting properties
of the model, yet makes the theory as a whole much more tractable. Accordingly,
we produce novel expressions for the two and four-point correlators at
arbitrary temperature and find the surprising result they take a universal
closed form. We note that these expressions correctly match onto and
interpolate between previously-obtained low-energy results and simple
high-energy perturbative checks. We find that the time-ordered four-point
correlators are always determined by finite temperature OPEs into the identity
and Hamiltonian, while the out-of-time-order four-point correlators remain
nontrivial and always scramble. This has only been established in the conformal
limit, so to find that it holds for large q at all temperatures/couplings is a
nontrivial result. Finally, we determine the system's thermalization and
scrambling rates and find that they always agree, regardless of temperature.
This adds to the increasing body of evidence that there exists simple
structures in large N internal dynamics, such as those formed by SYK's epidemic
operator growth.
