We show that scalar quantum field theory in four space-time dimensions with global O(N)3 symmetry and imaginary tetrahedral coupling is asymptotically free and bounded from below in the large-N limit. 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, such as the possible existence of quantum bounds on dynamical observables in strongly coupled field theories, from first principles.
J. Berges, R. Gurau, T. Preis, “Asymptotic freedom in a strongly interacting scalar quantum field theory in four space-time dimensions”, arXiv:2301.09514 (2023).
Related to Project B03