Gradient flow of O(N) nonlinear sigma model at large N
Here, 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.
 Authors:

^{[1]};
^{[1]};
^{[2]}
 Kyoto Univ., Kyoto (Japan). Yukawa Inst. for Theoretical Physics
 Osaka Univ., Toyonaka (Japan). Dept. of Physics
 Publication Date:
 Grant/Contract Number:
 SC0011941
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of High Energy Physics (Online)
 Additional Journal Information:
 Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2015; Journal Issue: 4; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Research Org:
 Columbia Univ., New York, NY (United States)
 Sponsoring Org:
 USDOE Office of Science (SC)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Lattice Quantum Field Theory; Field Theories in Lower Dimensions; Nonperturbative Effects
 OSTI Identifier:
 1454542
Aoki, Sinya, Kikuchi, Kengo, and Onogi, Tetsuya. Gradient flow of O(N) nonlinear sigma model at large N. United States: N. p.,
Web. doi:10.1007/JHEP04(2015)156.
Aoki, Sinya, Kikuchi, Kengo, & Onogi, Tetsuya. Gradient flow of O(N) nonlinear sigma model at large N. United States. doi:10.1007/JHEP04(2015)156.
Aoki, Sinya, Kikuchi, Kengo, and Onogi, Tetsuya. 2015.
"Gradient flow of O(N) nonlinear sigma model at large N". United States.
doi:10.1007/JHEP04(2015)156. https://www.osti.gov/servlets/purl/1454542.
@article{osti_1454542,
title = {Gradient flow of O(N) nonlinear sigma model at large N},
author = {Aoki, Sinya and Kikuchi, Kengo and Onogi, Tetsuya},
abstractNote = {Here, 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.},
doi = {10.1007/JHEP04(2015)156},
journal = {Journal of High Energy Physics (Online)},
number = 4,
volume = 2015,
place = {United States},
year = {2015},
month = {4}
}