Fixed point structure of the gradient flow exact renormalization group for scalar field theories. (31st January 2022)

• Record Type: Journal Article
• Authors: Abe, Yoshihiko; Hamada, Yu; Haruna, Junichi
• Is Part Of: Progress of theoretical and experimental physics. Volume 2022:Number 3(2022)
• Publication Date: 2022-01-31
• Subjects: B06 -- B32 -- B37; Physics -- Periodicals; Mathematical physics -- Periodicals; 530.05
• DOI: 10.1093/ptep/ptac021
• Languages: English
• ISSNs: 2050-3911

Abstract

Abstract: The gradient flow exact renormalization group (GFERG) is a framework for defining the Wilson action via a gradient flow equation. We study the fixed point structure of the GFERG equation associated with a general gradient flow equation for scalar field theories, and show that it is the same as that of the conventional Wilson–Polchinski (WP) equation in general. Furthermore, we see that the GFERG equation has a similar RG flow structure around a fixed point to the WP equation. We illustrate these results with the O ( N ) non-linear sigma model in 4 − ϵ dimensions and the Wilson–Fisher fixed point.