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Implementing Wilsonian renormalization group transformations in an iterativeway, we develop a non-perturbative field theoretical framework, which takesinto account all-loop quantum corrections organized in the $1/N$ expansion,where $N$ represents the flavor number of quantum fields. The resultingclassical field theory is given by an effective Landau-Ginzburg theory for alocal order parameter field, which appears in one-dimensional higher spacetime.We claim that such all-loop quantum corrections are introduced into an equationof motion for the order parameter field through the evolution in the emergentextra dimension. Based on this non-perturbative theoretical framework, we solvethe Kondo effect, where the quantum mechanics problem in the projectiveformulation is mapped into a Landau-Ginzburg field theory for the hybridizationorder parameter field with an emergent extra dimension. We confirm thenon-perturbative nature of this field theoretical framework. Intriguingly, weshow that the Wilsonian renormalization group method can explainnon-perturbative thermodynamic properties of an impurity consistent with theBethe ansatz solutions. Finally, we speculate how our non-perturbative fieldtheoretical framework can be connected with the AdS$_{d+2}$/CFT$_{d+1}$ dualityconjecture.

physical review. d/physical review. d.

A non-perturbative field theory approach for the Kondo effect: Emergence  of an extra dimension and its implication for the holographic duality  conjecture