2014/12/31 by Sinya Aoki, Kengo Kikuchi, T. Onogi +1
Mathematics · Physics and Astronomy · #Applied mathematics #Balanced flow #Black Holes and Theoretical Physics #Coupling (piping) #Field (mathematics) #Flow (mathematics) #Function (biology) #High-Energy Particle Collisions Research #Mathematical analysis #Mathematical physics #Mathematics #Mechanics #Nonlinear system #Physics #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Sigma #Sigma model #hep-lat #hep-th
paper · pdf · doi:10.1007/jhep04(2015)156
published as JHEP 1504 (2015) 156 · 21 pages; v2: minor corrections, added references and note, v3: published version
openalex publication_date 2015/04/01 · arxiv created 2015/05/03 · arxiv updated 2015/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the gradient flow equation for the O(N) nonlinear sigma model in two dimensions at large N. We parameterize solution of the field at flow time t in powers of bare fields by introducing the coefficient function X n for the n-th power term (n = 1, 3, ··· ). Reducing the flow equation by keeping only the contributions at leading order in large N, we obtain a set of equations for X n ’s, which can be solved iteratively starting from n = 1. For n = 1 case, we find an explicit form of the exact solution. Using this solution, we show that the two point function at finite flow time t is finite. As an application, we obtain the non-perturbative running coupling defined from the energy density. We also discuss the solution for n = 3 case.