Long-range multi-scalar models at three loops
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2020
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| _version_ | 1866909377198292992 |
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| author | Benedetti, Dario Gurau, Razvan Harribey, Sabine Suzuki, Kenta |
| author_facet | Benedetti, Dario Gurau, Razvan Harribey, Sabine Suzuki, Kenta |
| contents | We compute the three-loop beta functions of long-range multi-scalar models with general quartic interactions. The long-range nature of the models is encoded in a kinetic term with a Laplacian to the power $0<ζ<1$, rendering the computation of Feynman diagrams much harder than in the usual short-range case ($ζ=1$). As a consequence, previous results stopped at two loops, while six-loop results are available for short-range models. We push the renormalization group analysis to three loops, in an $ε=4ζ-d$ expansion at fixed dimension $d<4$, extensively using the Mellin-Barnes representation of Feynman amplitudes in the Schwinger parametrization. We then specialize the beta functions to various models with different symmetry groups: $O(N)$, $(\mathbb{Z}_2)^N \rtimes S_N$, and $O(N)\times O(M)$. For such models, we compute the fixed points and critical exponents. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2007_04603 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Long-range multi-scalar models at three loops Benedetti, Dario Gurau, Razvan Harribey, Sabine Suzuki, Kenta High Energy Physics - Theory Statistical Mechanics We compute the three-loop beta functions of long-range multi-scalar models with general quartic interactions. The long-range nature of the models is encoded in a kinetic term with a Laplacian to the power $0<ζ<1$, rendering the computation of Feynman diagrams much harder than in the usual short-range case ($ζ=1$). As a consequence, previous results stopped at two loops, while six-loop results are available for short-range models. We push the renormalization group analysis to three loops, in an $ε=4ζ-d$ expansion at fixed dimension $d<4$, extensively using the Mellin-Barnes representation of Feynman amplitudes in the Schwinger parametrization. We then specialize the beta functions to various models with different symmetry groups: $O(N)$, $(\mathbb{Z}_2)^N \rtimes S_N$, and $O(N)\times O(M)$. For such models, we compute the fixed points and critical exponents. |
| title | Long-range multi-scalar models at three loops |
| topic | High Energy Physics - Theory Statistical Mechanics |
| url | https://arxiv.org/abs/2007.04603 |