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 nontrivial dynamics, such as direct scattering, while still being analytically tractable also nonperturbatively. Our findings open up a way to address outstanding problems in strongly coupled theories from first principles.
J. Berges, R. Gurau, T. Preis, “Asymptotic freedom in a strongly interacting scalar quantum field theory in four Euclidean dimensions”, Phys. Rev. D 108, 016019 (2023).
Related to Project B03