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arXiv · 2301.09514

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

Jürgen Berges·Razvan Gurau·Thimo Preis
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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.

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Jürgen Berges, Razvan Gurau, Thimo Preis. 2023-01-23. Asymptotic freedom in a strongly interacting scalar quantum field theory in four Euclidean dimensions. https://doi.org/10.1103/physrevd.108.016019

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