Exact Results for the Spectrum of the Ising Conformal Field Theory
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918196503642112 |
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| author | Antipin, Oleg Bersini, Jahmall Hafjall, Jacob Muco, Giulia Sannino, Francesco |
| author_facet | Antipin, Oleg Bersini, Jahmall Hafjall, Jacob Muco, Giulia Sannino, Francesco |
| contents | We develop a semiclassical framework to determine scaling dimensions of neutral composite operators in scalar conformal field theories. For the critical Ising $λϕ^4$ theory in $d=4-ε$, we obtain the full spectrum of composite operators built out of $n$ fields transforming in the traceless-symmetric Lorentz representations to next-to-leading order in the double-scaling limit $n\rightarrow \infty$ and $λ\rightarrow 0$ with $λn$ fixed. At any given order the semiclassical expansion resums an infinite number of Feynman diagrams. Combining our results with existing perturbative computations further yields the complete five-loop scaling dimensions in the $ε$-expansion for the family of $ϕ^n$ operators. Finally, in three dimensions the next-to-leading order semiclassical results supersede any other existing methodology for $n \gtrsim \mathcal{O}(10)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_08276 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exact Results for the Spectrum of the Ising Conformal Field Theory Antipin, Oleg Bersini, Jahmall Hafjall, Jacob Muco, Giulia Sannino, Francesco High Energy Physics - Theory Strongly Correlated Electrons High Energy Physics - Phenomenology We develop a semiclassical framework to determine scaling dimensions of neutral composite operators in scalar conformal field theories. For the critical Ising $λϕ^4$ theory in $d=4-ε$, we obtain the full spectrum of composite operators built out of $n$ fields transforming in the traceless-symmetric Lorentz representations to next-to-leading order in the double-scaling limit $n\rightarrow \infty$ and $λ\rightarrow 0$ with $λn$ fixed. At any given order the semiclassical expansion resums an infinite number of Feynman diagrams. Combining our results with existing perturbative computations further yields the complete five-loop scaling dimensions in the $ε$-expansion for the family of $ϕ^n$ operators. Finally, in three dimensions the next-to-leading order semiclassical results supersede any other existing methodology for $n \gtrsim \mathcal{O}(10)$. |
| title | Exact Results for the Spectrum of the Ising Conformal Field Theory |
| topic | High Energy Physics - Theory Strongly Correlated Electrons High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2511.08276 |