Sextic tensor model in rank 3 at next-to-leading order

• Verfasst von: Harribey, Sabine [VerfasserIn]
• Titel: Sextic tensor model in rank 3 at next-to-leading order
• Verf.angabe: Sabine Harribey
• E-Jahr: 2021
• Jahr: 16 Sep 2021
• Umfang: 23 S.
• Fussnoten: Gesehen am 28.09.2022
• Titel Quelle: Enthalten in: De.arxiv.org
• Ort Quelle: [S.l.] : Arxiv.org, 1991
• Jahr Quelle: 2021
• Band/Heft Quelle: (2021), Artikel-ID 2109.08034, Seite 1-23
• DOI: doi:10.48550/arXiv.2109.08034
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: High Energy Physics - Theory
• K10plus-PPN: 1817221116

Abstract

We compute the four-loop beta functions of short and long-range multi scalar models with general sextic interactions and complex fields. We then specialize the beta functions to a $U(N)^3$ symmetry and study the renormalization group at next-to-leading order in $N$ and small $\epsilon$. In the short-range case, $\epsilon$ is the deviation from the critical dimension while it is the deviation from the critical scaling of the free propagator in the long-range case. This allows us to find the $1/N$ corrections to the rank-3 sextic tensor model of arXiv:1912.06641. In the short-range case, we still find a non-trivial real IR stable fixed point, with a diagonalizable stability matrix. All couplings, except for the so-called wheel coupling, have terms of order $\epsilon^0$ at leading and next-to-leading order, which makes this fixed point different from the other melonic fixed points found in quartic models. In the long-range case, the corrections to the fixed point are instead not perturbative in $\epsilon$ and hence unreliable; we thus find no precursor of the large-$N$ fixed point.