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Title: Gradient flow of O(N) nonlinear sigma model at large N

Journal Article · · Journal of High Energy Physics (Online)
 [1];  [1];  [2]
  1. Kyoto Univ., Kyoto (Japan). Yukawa Inst. for Theoretical Physics
  2. Osaka Univ., Toyonaka (Japan). Dept. of Physics
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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.

Research Organization:
Columbia Univ., New York, NY (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
Grant/Contract Number:
SC0011941
OSTI ID:
1454542
Journal Information:
Journal of High Energy Physics (Online), Vol. 2015, Issue 4; ISSN 1029-8479
Publisher:
Springer BerlinCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 7 works
Citation information provided by
Web of Science

References (12)

Chiral symmetry and the Yang-Mills gradient flow journal April 2013
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The lattice gradient flow at tree-level and its improvement journal September 2014
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Space-time symmetries and the Yang-Mills gradient flow journal November 2013
Generalized gradient flow equation and its application to super Yang-Mills theory journal November 2014
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High-precision scale setting in lattice QCD journal September 2012
Drastic reduction of cutoff effects in 2-d lattice O(N) models journal November 2012

Cited By (3)

Geometries from field theories journal October 2015
Flow equation for the large N scalar model and induced geometries journal August 2016
Geometries from field theories text January 2015

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Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Lattice Quantum Field Theory
Field Theories in Lower Dimensions
Nonperturbative Effects