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Two-point functions in a holographic Kondo model

  • Johanna ErdmengerEmail author
  • Carlos Hoyos
  • Andy O’Bannon
  • Ioannis Papadimitriou
  • Jonas Probst
  • Jackson M. S. Wu
Open Access
Regular Article - Theoretical Physics

Abstract

We develop the formalism of holographic renormalization to compute two-point functions in a holographic Kondo model. The model describes a (0 + 1)-dimensional impurity spin of a gauged SU(N ) interacting with a (1 + 1)-dimensional, large-N , strongly-coupled Conformal Field Theory (CFT). We describe the impurity using Abrikosov pseudo-fermions, and define an SU(N )-invariant scalar operator \( \mathcal{O} \) built from a pseudo-fermion and a CFT fermion. At large N the Kondo interaction is of the form \( {\mathcal{O}}^{\dagger}\mathcal{O} \), which is marginally relevant, and generates a Renormalization Group (RG) flow at the impurity. A second-order mean-field phase transition occurs in which \( \mathcal{O} \) condenses below a critical temperature, leading to the Kondo effect, including screening of the impurity. Via holography, the phase transition is dual to holographic superconductivity in (1 + 1)-dimensional Anti-de Sitter space. At all temperatures, spectral functions of \( \mathcal{O} \) exhibit a Fano resonance, characteristic of a continuum of states interacting with an isolated resonance. In contrast to Fano resonances observed for example in quantum dots, our continuum and resonance arise from a (0 + 1)-dimensional UV fixed point and RG flow, respectively. In the low-temperature phase, the resonance comes from a pole in the Green’s function of the form −i\( \mathcal{O} \)2, which is characteristic of a Kondo resonance.

Keywords

Holography and condensed matter physics (AdS/CMT) AdS-CFT Correspondence Gauge-gravity correspondence 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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© The Author(s) 2017

Authors and Affiliations

  1. 1.Institut für Theoretische Physik und AstrophysikJulius-Maximilians-Universität WürzburgWürzburgGermany
  2. 2.Max-Planck-Institut für Physik (Werner-Heisenberg-Institut)MunichGermany
  3. 3.Department of PhysicsUniversidad de OviedoOviedoSpain
  4. 4.STAG Research Centre, Physics and AstronomyUniversity of SouthamptonSouthamptonU.K.
  5. 5.SISSA and INFN — Sezione di TriesteTriesteItaly
  6. 6.Rudolf Peierls Centre for Theoretical PhysicsUniversity of OxfordOxfordU.K.
  7. 7.Department of Physics and AstronomyUniversity of AlabamaTuscaloosaU.S.A.

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