A new method to solve the Non Perturbative Renormalization Group equations

Abstract

We propose a method to solve the Non Perturbative Renormalization Group equations for the $n$-point functions. In leading order, it consists in solving the equations obtained by closing the infinite hierarchy of equations for the $n$-point functions. This is achieved: i) by exploiting the decoupling of modes and the analyticity of the $n$-point functions at small momenta: this allows us to neglect some momentum dependence of the vertices entering the flow equations; ii) by relating vertices at zero momenta to derivatives of lower order vertices with respect to a constant background field. Although the approximation is not controlled by a small parameter, its accuracy can be systematically improved. When it is applied to the O(N) model, its leading order is exact in the large $N$ limit; in this case, one recovers known results in a simple and direct way, i.e., without introducing an auxiliary field.

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References in corpus (5)

• Renormalization flow of Yang-Mills propagators
• Non perturbative renormalization group and momentum dependence of n-point functions (II)
• Non Perturbative Renormalization Group, momentum dependence of $n$-point functions and the transition temperature of the weakly interacting Bose gas
• Non-Perturbative Renormalization Group calculation of the scalar self-energy
• Infrared Non-perturbative Propagators of Gluon and Ghost via Exact Renormalization Group

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