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

TL;DR

This paper demonstrates that a specific four-dimensional scalar quantum field theory with a certain symmetry and imaginary coupling is asymptotically free and well-behaved at large N, providing a new solvable model for strongly coupled dynamics.

Contribution

It introduces a novel scalar quantum field theory with imaginary tetrahedral coupling that is asymptotically free and analytically tractable at large N, expanding the landscape of solvable strongly interacting models.

Findings

The theory is asymptotically free in four dimensions.

The quantum effective action depends only on the real square of the coupling.

The renormalization group flow connects Gaussian and strongly interacting fixed points.

Abstract

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.