Long-range multi-scalar models at three loops
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 sh...
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| Main Authors: | , , , |
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| Format: | Article (Journal) Chapter/Article |
| Language: | English |
| Published: |
28 Oct 2020
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| In: |
Arxiv
Year: 2020, Pages: 1-39 |
| DOI: | 10.48550/arXiv.2007.04603 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.48550/arXiv.2007.04603
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| Author Notes: | Dario Benedetti, Razvan Gurau, Sabine Harribey, and Kenta Suzuki |
| Summary: | 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 seven-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), , and O(N) × O(M). For such models, we compute the fixed points and critical exponents. |
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| Item Description: | Version 1 vom 9. Juli 2020, Version 2 vom 28. Oktober 2020 Gesehen am 07.10.2022 |
| Physical Description: | Online Resource |
| DOI: | 10.48550/arXiv.2007.04603 |