#paperOfTheDay : "What if phi^4 theory in 4 dimensions is non-trivial in the continuum?" From 2023. It is widely accepted that the scalar field theory with quartic interaction is trivial in 4 spacetime dimensions. This means: In the renormalization group, the coupling increases logarithmically when the energy scale increases, and therefore, if one believes that the theory is valid at infinitely high energy (i.e. in the continuum, without lattice regularization the grenormalized coupling should be finite), then its coupling must be zero at lower energy, and therefore the theory is effectively equal to a free theory.
The present article seemingly avoids this problem by allowing the coupling to be negative. Normally, this would lead to a non-unitary theory, but apparently some work exists to make sense of this situation (I should read that next). What bothers me more is the presence of a Landau pole: Morally, the coupling behaves similar to 1/(1-x) where x is the energy scale: It is positive for small x, and goes to zero (albeit being negative) for very large x, but it has a pole at x=1, hence there is an intermediate theory with infinite coupling, which I find a bit problematic without further analysis. The article acknowledges this fact, but apparently isn't bothered too much. I do believe that this is an interesting question with potentially fascinating consequences, but I would like to understand the role of the Landau pole better.
https://arxiv.org/abs/2305.05678