2018/05/31 by Yoshihiko Abe, Masafumi Fukuma · 43 citations
Engineering · Physics and Astronomy · #Action (physics) #Balanced flow #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Effective action #Eigenvalues and eigenvectors #Flow (mathematics) #Fluid dynamics and aerodynamics studies #Kinetic term #Renormalization #Renormalization group #Scalar (mathematics) #Scalar field theory #hep-lat #hep-th
paper · pdf · doi:10.1093/ptep/pty081
published in Progress of Theoretical and Experimental Physics 2018(8) (University of Oxford) · 11 pages, 1 figure; v2, v3: typos corrected, some discussions improved
openalex created_date 2018/06/13 · arxiv created 2018/07/02 · openalex publication_date 2018/07/04 · arxiv updated 2019/12/06 · openalex updated_date 2026/08/05
We investigate the renormalization group (RG) structure of the gradient flow. Instead of using the original bare action to generate the flow, we propose to use the effective action at each flow time. We write down the basic equation for scalar field theory that determines the evolution of the action, and argue that the equation can be regarded as an RG equation if one makes a field-variable transformation at every step such that the kinetic term is kept in the canonical form. We consider a local potential approximation (LPA) to our equation, and show that the result has a natural interpretation with Feynman diagrams. We make an |ε| expansion of the LPA and show that it reproduces the eigenvalues of the linearized RG transformation around both the Gaussian and the Wilson–Fisher fixed points to the order of |ε|.