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

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arxiv 2301.09514 v2 pith:TNTS35T7 submitted 2023-01-23 hep-th hep-ph

Jürgen Berges , Razvan Gurau , Thimo Preis This is my paper · ORCID
classification hep-thhep-ph
keywords theoryfieldquantumstronglycouplingdimensionseuclideanfour
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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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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. $F$-extremization determines certain large-$N$ CFTs

    hep-th 2024-12 conditional novelty 7.0 of 10

    Melonic large-N CFTs are exactly the conformal mean field theories that extremize the universal part of the sphere free energy under linear IR marginality constraints.

  2. Asymptotic safety meets tensor field theory: towards a new class of gravity-matter systems

    hep-th 2025-01 conditional novelty 6.0 of 10

    Adding asymptotically safe gravity to the O(N)^3 tensor field theory converts its asymptotic freedom into an interacting fixed point at a non-zero quartic coupling.

  3. On the negative coupling O(N) model in 2d at high temperature

    hep-th 2024-12 conditional novelty 6.0 of 10

    For the 2d negative-coupling O(N) model at large N, the correct vacuum is a saddle point on a non-principal Riemann sheet, giving a real free energy and dynamical stability at all temperatures.

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