Long-range multi-scalar models at three loops

• Verfasst von: Benedetti, Dario [VerfasserIn]
• Verfasst von: Gurǎu, Rǎzvan [VerfasserIn]
• Verfasst von: Harribey, Sabine [VerfasserIn]
• Verfasst von: Suzuki, Kenta [VerfasserIn]
• Titel: Long-range multi-scalar models at three loops
• Verf.angabe: Dario Benedetti, Razvan Gurau, Sabine Harribey, and Kenta Suzuki
• E-Jahr: 2020
• Jahr: 28 Oct 2020
• Umfang: 39 S.
• Fussnoten: Version 1 vom 9. Juli 2020, Version 2 vom 28. Oktober 2020 ; Gesehen am 07.10.2022
• Titel Quelle: Enthalten in: De.arxiv.org
• Ort Quelle: [S.l.] : Arxiv.org, 1991
• Jahr Quelle: 2020
• Band/Heft Quelle: (2020), Artikel-ID 2007.04603, Seite 1-39
• DOI: doi:10.48550/arXiv.2007.04603
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1804434353

Abstract

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.