Two-point Functions in a Holographic Kondo Model

Erdmenger, Johanna; Hoyos, Carlos; O'Bannon, Andy; Papadimitriou, Ioannis; Probst, Jonas; Wu, Jackson M.S.

doi:10.1007/JHEP03(2017)039

Two-point Functions in a Holographic Kondo Model

Johanna Erdmenger
(
- Wurzburg U. and
- Munich, Max Planck Inst.
)
,
Carlos Hoyos
(
- Oviedo U.
)
,
Andy O'Bannon
(
- Southampton U.
)
,
Ioannis Papadimitriou
(
- INFN, Trieste and
- SISSA, Trieste
)
,
Jonas Probst
(
- Oxford U., Theor. Phys.
)

Dec 6, 2016

65 pages

Published in:

JHEP 03 (2017) 039

Published: Mar 7, 2017

e-Print:

1612.02005 [hep-th]

DOI:

10.1007/JHEP03(2017)039

Report number:

OUTP-16-27P,
SISSA-61-2016-FISI,
FPAUO-16-16

View in:

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Abstract: (Springer)

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.

Note:

65 pages, 17 figures; v2 minor improvements. Version published in JHEP

Holography and condensed matter physics (AdS/CMT)
AdS-CFT Correspondence
Gauge-gravity correspondence
field theory: conformal
superconductivity: holography
renormalization group: flow
critical phenomena
two-point function
Kondo model
SU(N)

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