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

## TL;DR

This paper develops a non-perturbative field theory framework using Wilsonian renormalization to analyze the Kondo effect, revealing an emergent extra dimension and exploring its implications for holographic duality.

## Contribution

It introduces a novel non-perturbative approach incorporating all-loop quantum corrections via an emergent extra dimension, linking Kondo physics with holographic duality.

## Key findings

- Successfully maps the Kondo effect to a Landau-Ginzburg theory with an extra dimension.
- Explains non-perturbative thermodynamics consistent with Bethe ansatz.
- Suggests a connection between the framework and AdS/CFT duality.

## Abstract

Implementing Wilsonian renormalization group transformations in an iterative way, we develop a non-perturbative field theoretical framework, which takes into account all-loop quantum corrections organized in the $1/N$ expansion, where $N$ represents the flavor number of quantum fields. The resulting classical field theory is given by an effective Landau-Ginzburg theory for a local order parameter field, which appears in one-dimensional higher spacetime. We claim that such all-loop quantum corrections are introduced into an equation of motion for the order parameter field through the evolution in the emergent extra dimension. Based on this non-perturbative theoretical framework, we solve the Kondo effect, where the quantum mechanics problem in the projective formulation is mapped into a Landau-Ginzburg field theory for the hybridization order parameter field with an emergent extra dimension. We confirm the non-perturbative nature of this field theoretical framework. Intriguingly, we show that the Wilsonian renormalization group method can explain non-perturbative thermodynamic properties of an impurity consistent with the Bethe ansatz solutions. Finally, we speculate how our non-perturbative field theoretical framework can be connected with the AdS$_{d+2}$/CFT$_{d+1}$ duality conjecture.