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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| Hauptverfasser: | , , , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
15 October 2020
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| In: |
Journal of physics. A, Mathematical and theoretical
Year: 2020, Jahrgang: 53, Heft: 44, Pages: ? |
| ISSN: | 1751-8121 |
| DOI: | 10.1088/1751-8121/abb6ae |
| Online-Zugang: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1088/1751-8121/abb6ae
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| Verfasserangaben: | Dario Benedetti, Razvan Gurau, Sabine Harribey, and Kenta Suzuki |
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| 520 | |a 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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