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arXiv · 1705.06571

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

Ki-Seok Kim·Suk Bum Chung·Chanyong Park·Jaeho Han
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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.

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Ki-Seok Kim, Suk Bum Chung, Chanyong Park, Jaeho Han. 2017-05-18. A non-perturbative field theory approach for the Kondo effect: Emergence of an extra dimension and its implication for the holographic duality conjecture. https://doi.org/10.1103/physrevd.99.105012

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