On the six-loop scaling dimensions of the $(ϕ^2)^n$ operators in $d=3$
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| Format: | Preprint |
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2025
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| _version_ | 1866908904131133440 |
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| author | Bednyakov, A. V. Kompaniets, M. V. Trenogin, A. V. |
| author_facet | Bednyakov, A. V. Kompaniets, M. V. Trenogin, A. V. |
| contents | We consider a class of singlet operators $(ϕ^2)^n$ in the three-dimensional $O(N)$ model with $λ^2 ϕ^6$ interaction. Recently, the corresponding anomalous dimensions $γ_{2n}$ were computed by semiclassical methods and the all-loop result for the leading-$n$ corrections in the small $λ$ limit was found. In this paper, we obtain the six-loop expressions not only for the leading-$n$ contribution but also for the subleading one. While the leading correction confirms the predictions of recent semiclassical calculation, the subleading one is a new result and will serve as a future welcome check for all-loop expressions. As an important by-product of our calculation, we provide a full dependence on $n$ of the four-loop $γ_{2n}$ in the $O(N)$ case. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_05059 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the six-loop scaling dimensions of the $(ϕ^2)^n$ operators in $d=3$ Bednyakov, A. V. Kompaniets, M. V. Trenogin, A. V. High Energy Physics - Theory Statistical Mechanics We consider a class of singlet operators $(ϕ^2)^n$ in the three-dimensional $O(N)$ model with $λ^2 ϕ^6$ interaction. Recently, the corresponding anomalous dimensions $γ_{2n}$ were computed by semiclassical methods and the all-loop result for the leading-$n$ corrections in the small $λ$ limit was found. In this paper, we obtain the six-loop expressions not only for the leading-$n$ contribution but also for the subleading one. While the leading correction confirms the predictions of recent semiclassical calculation, the subleading one is a new result and will serve as a future welcome check for all-loop expressions. As an important by-product of our calculation, we provide a full dependence on $n$ of the four-loop $γ_{2n}$ in the $O(N)$ case. |
| title | On the six-loop scaling dimensions of the $(ϕ^2)^n$ operators in $d=3$ |
| topic | High Energy Physics - Theory Statistical Mechanics |
| url | https://arxiv.org/abs/2512.05059 |