%0 Journal Article
%T Gradient Flow of O(N) nonlinear sigma model at large N
%A Sinya Aoki
%A Kengo Kikuchi
%A Tetsuya Onogi
%J Physics
%D 2014
%I arXiv
%R 10.1007/JHEP04(2015)156
%X 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.
%U http://arxiv.org/abs/1412.8249v3