  We show that scalar quantum field theory in four Euclidean dimensions with
global $O(N)^3$ symmetry and imaginary tetrahedral coupling is asymptotically
free and bounded from below in the large-N limit. While the Hamiltonian is
non-Hermitian, the full quantum effective action for the large-N theory only
depends on the square of that coupling which is real. A perturbative analysis
uncovers that the renormalization group flow of the quartic couplings connects
a Gaussian ultraviolet fixed point to a strongly interacting theory in the
infrared. This realizes a renormalizable field theory which exhibits
non-trivial dynamics, such as direct scattering, while still being analytically
tractable also non-perturbatively. Our findings open up a way to address
outstanding problems in strongly coupled theories from first principles.
