Gradient Flow of O(N) nonlinear sigma model at large N

Abstract

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.

arXiv comment21 pages; v2: minor corrections, added references and note, v3: published version

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• Nonperturbative Renormalization of Operators in Near-Conformal Systems Using Gradient Flows
• Renormalizability of the gradient flow in the 2D $O(N)$ non-linear sigma model
• Proof of the renormalizability of the gradient flow
• Determination of Reference Scales for Wilson Gauge Action from Yang--Mills Gradient Flow
• Gradient flow exact renormalization group
• Background field method in the gradient flow
• Geometries from field theories
• The Yang-Mills gradient flow and lattice effective action
• Fixed Point Structure of Gradient Flow Exact Renormalization Group for Scalar Field Theories
• Supersymmetric gradient flow in the Wess-Zumino model
• Flow Equation of N=1 Supersymmetric O(N) Nonlinear Sigma Model in Two Dimensions
• Encoding field theories into gravities
• Axial $U(1)$ anomaly in a gravitational field via the gradient flow
• Functional Renormalization Group Analysis of $O(3)$ Nonlinear Sigma Model and Non-Abelian Bosonization Duality
• Perturbative analysis of the Wess-Zumino flow
• Flow equation for the large $N$ scalar model and induced geometries
• Gradient-flowed order parameter for spontaneous gauge symmetry breaking
• Generalized Gradient Flow Equation and Its Applications