Gradient flow of O(N) nonlinear sigma model at large N
Abstract
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 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.
- Authors:
-
- Kyoto Univ., Kyoto (Japan). Yukawa Inst. for Theoretical Physics
- Osaka Univ., Toyonaka (Japan). Dept. of Physics
- Publication Date:
- Research Org.:
- Columbia Univ., New York, NY (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1454542
- Grant/Contract Number:
- SC0011941
- Resource 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 1029-8479
- Publisher:
- Springer Berlin
- 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
Citation Formats
Aoki, Sinya, Kikuchi, Kengo, and Onogi, Tetsuya. Gradient flow of O(N) nonlinear sigma model at large N. United States: N. p., 2015.
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. https://doi.org/10.1007/JHEP04(2015)156
Aoki, Sinya, Kikuchi, Kengo, and Onogi, Tetsuya. Tue .
"Gradient flow of O(N) nonlinear sigma model at large N". United States. https://doi.org/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 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.},
doi = {10.1007/JHEP04(2015)156},
journal = {Journal of High Energy Physics (Online)},
number = 4,
volume = 2015,
place = {United States},
year = {Tue Apr 28 00:00:00 EDT 2015},
month = {Tue Apr 28 00:00:00 EDT 2015}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 7 works
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Chiral symmetry and the Yang-Mills gradient flow
journal, April 2013
- Lüscher, Martin
- Journal of High Energy Physics, Vol. 2013, Issue 4
Interaction of goldstone particles in two dimensions. Applications to ferromagnets and massive Yang-Mills fields
journal, October 1975
- Polyakov, A. M.
- Physics Letters B, Vol. 59, Issue 1
The Yang-Mills gradient flow in finite volume
journal, November 2012
- Fodor, Zoltan; Holland, Kieran; Kuti, Julius
- Journal of High Energy Physics, Vol. 2012, Issue 11
The gradient flow coupling in the Schrödinger functional
journal, October 2013
- Fritzsch, Patrick; Ramos, Alberto
- Journal of High Energy Physics, Vol. 2013, Issue 10
The lattice gradient flow at tree-level and its improvement
journal, September 2014
- Fodor, Zoltan; Holland, Kieran; Kuti, Julius
- Journal of High Energy Physics, Vol. 2014, Issue 9
Properties and uses of the Wilson flow in lattice QCD
journal, August 2010
- Lüscher, Martin
- Journal of High Energy Physics, Vol. 2010, Issue 8
Space-time symmetries and the Yang-Mills gradient flow
journal, November 2013
- Del Debbio, L.; Patella, A.; Rago, A.
- Journal of High Energy Physics, Vol. 2013, Issue 11
Generalized gradient flow equation and its application to super Yang-Mills theory
journal, November 2014
- Kikuchi, Kengo; Onogi, Tetsuya
- Journal of High Energy Physics, Vol. 2014, Issue 11
Trivializing Maps, the Wilson Flow and the HMC Algorithm
journal, November 2009
- Lüscher, Martin
- Communications in Mathematical Physics, Vol. 293, Issue 3
High-precision scale setting in lattice QCD
journal, September 2012
- Borsányi, Szabolcs; Dürr, Stephan; Fodor, Zoltán
- Journal of High Energy Physics, Vol. 2012, Issue 9
Drastic reduction of cutoff effects in 2-d lattice O(N) models
journal, November 2012
- Balog, J.; Niedermayer, F.; Pepe, M.
- Journal of High Energy Physics, Vol. 2012, Issue 11
Works referencing / citing this record:
Geometries from field theories
journal, October 2015
- Aoki, Sinya; Kikuchi, Kengo; Onogi, Tetsuya
- Progress of Theoretical and Experimental Physics, Vol. 2015, Issue 10
Flow equation for the large N scalar model and induced geometries
journal, August 2016
- Aoki, Sinya; Balog, Janos; Onogi, Tetsuya
- Progress of Theoretical and Experimental Physics, Vol. 2016, Issue 8