{"title":"Recent Progress in Asymptotic Safety","authors":"Alfiia Mukhaeva","doi":"10.1134/S106377882470100X","DOIUrl":null,"url":null,"abstract":"<p>Free and interacting fixed points of the renormalization group play an important role in particle and statistical physics. High energy fixed points such as in asymptotic freedom or asymptotic safety are crucial for a fundamental definition of quantum field theory. Low energy fixed points relate to (quantum) phase transitions and critical phenomena. In this contribution, we explain the arising of weakly interacting fixed points in general 4d QFTs. This covers necessary and sufficient conditions for existence, and explicit examples. In addition, we also review the last progress in calculation of beta functions, anomalous dimensions up to four loop in the gauge and three loop in the Yukawa and scalar couplings. Moreover, we will overview the status of functional renormalization group and its implications for gravity.</p>","PeriodicalId":728,"journal":{"name":"Physics of Atomic Nuclei","volume":"87 3 supplement","pages":"S489 - S494"},"PeriodicalIF":0.3000,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physics of Atomic Nuclei","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1134/S106377882470100X","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"PHYSICS, NUCLEAR","Score":null,"Total":0}
引用次数: 0
Abstract
Free and interacting fixed points of the renormalization group play an important role in particle and statistical physics. High energy fixed points such as in asymptotic freedom or asymptotic safety are crucial for a fundamental definition of quantum field theory. Low energy fixed points relate to (quantum) phase transitions and critical phenomena. In this contribution, we explain the arising of weakly interacting fixed points in general 4d QFTs. This covers necessary and sufficient conditions for existence, and explicit examples. In addition, we also review the last progress in calculation of beta functions, anomalous dimensions up to four loop in the gauge and three loop in the Yukawa and scalar couplings. Moreover, we will overview the status of functional renormalization group and its implications for gravity.
期刊介绍：
Physics of Atomic Nuclei is a journal that covers experimental and theoretical studies of nuclear physics: nuclear structure, spectra, and properties; radiation, fission, and nuclear reactions induced by photons, leptons, hadrons, and nuclei; fundamental interactions and symmetries; hadrons (with light, strange, charm, and bottom quarks); particle collisions at high and superhigh energies; gauge and unified quantum field theories, quark models, supersymmetry and supergravity, astrophysics and cosmology.
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