
Gradient flow of O(N) nonlinear sigma model at large NGradient flow of O(N) nonlinear sigma model at large N 
"/Aoki, Sinya/"Aoki, Sinya ,
"/Kikuchi, Kengo/"Kikuchi, Kengo ,
"/Onogi, Tetsuya/"Onogi, Tetsuya
2015
(
4
)
201504 , Springer Berlin Heidelberg
ISSN:10298479
Description
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 nth 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 nonperturbative running coupling defined from the energy density. We also discuss the solution for n = 3 case.
FullText
http://repository.kulib.kyotou.ac.jp/dspace/bitstream/2433/203070/1/JHEP04%282015%29156.pdf