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We show that scalar quantum field theory in four Euclidean dimensions withglobal $O(N)^3$ symmetry and imaginary tetrahedral coupling is asymptoticallyfree and bounded from below in the large-N limit. While the Hamiltonian isnon-Hermitian, the full quantum effective action for the large-N theory onlydepends on the square of that coupling which is real. A perturbative analysisuncovers that the renormalization group flow of the quartic couplings connectsa Gaussian ultraviolet fixed point to a strongly interacting theory in theinfrared. This realizes a renormalizable field theory which exhibitsnon-trivial dynamics, such as direct scattering, while still being analyticallytractable also non-perturbatively. Our findings open up a way to addressoutstanding problems in strongly coupled theories from first principles.

Asymptotic freedom in a strongly interacting scalar quantum field theory in four Euclidean dimensions