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arXiv · 2008.04077

On critical models with $N\leq 4$ scalars in $d=4-\epsilon$

Alessandro Codello·Mahmoud Safari·Gian Paolo Vacca·Omar Zanusso
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Abstract

We adopt a combination of analytical and numerical methods to study the renormalization group flow of the most general field theory with quartic interaction in $d=4-\epsilon$ with $N=3$ and $N=4$ scalars. For $N=3$, we find that it admits only three nondecomposable critical points: the Wilson-Fisher with $O(3)$ symmetry, the cubic with $H_3=(\mathbb{Z}_2)^3\rtimes S_3$ symmetry, and the biconical with $O(2)\times \mathbb{Z}_2$. For $N=4$, our analysis reveals the existence of new nontrivial solutions with discrete symmetries and with up to three distinct field anomalous dimensions.

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Alessandro Codello, Mahmoud Safari, Gian Paolo Vacca, Omar Zanusso. 2020-08-10. On critical models with $N\leq 4$ scalars in $d=4-\epsilon$. https://doi.org/10.1103/physrevd.102.065017

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