A maximally supersymmetric Kondo model

Abstract

We study the maximally supersymmetric Kondo model obtained by adding a fermionic impurity to N=4 supersymmetric Yang-Mills theory. While the original Kondo problem describes a defect interacting with a free Fermi liquid of itinerant electrons, here the ambient theory is an interacting CFT, and this introduces qualitatively new features into the system. The model arises in string theory by considering the intersection of a stack of M D5-branes with a stack of N D3-branes, at a point in the D3 worldvolume. We analyze the theory holographically, and propose a dictionary between the Kondo problem and antisymmetric Wilson loops in N=4 SYM. We perform an explicit calculation of the D5 fluctuations in the D3 geometry and determine the spectrum of defect operators. This establishes the stability of the Kondo fixed point together with its basic thermodynamic properties. Known supergravity solutions for Wilson loops allow us to go beyond the probe approximation: the D5s disappear and are replaced by three-form flux piercing a new topologically non-trivial three-sphere in the corrected geometry. This describes the Kondo model in terms of a geometric transition. A dual matrix model reflects the basic properties of the corrected gravity solution in its eigenvalue distribution.

46 pages, 2 figures. Minor typos corrected

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Cited by in corpus (34)

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• Charge transport by holographic Fermi surfaces
• A complexity/fidelity susceptibility g-theorem for AdS${}_3$/BCFT${}_2$
• Entanglement Entropy in a Holographic Kondo Model
• Hovering Black Holes from Charged Defects
• Holographic impurities and Kondo effect
• Holographic Kondo Model in Various Dimensions
• Supersymmetric Defect Models and Mirror Symmetry
• Two-point Functions in a Holographic Kondo Model
• Giant Wilson Loops and AdS${}_2$/dCFT${}_1$
• Moduli Spaces of Cold Holographic Matter
• Towards Holographic Spintronics
• Large rank Wilson loops in N=2 superconformal QCD at strong coupling
• Gravitational dual of the Rényi twist displacement operator
• Entanglement of heavy quark impurities and generalized gravitational entropy
• Holographic flows and thermodynamics of Polyakov loop impurities
• Impurities in Holography and Transport Coefficients
• Impurity-doped scalar fields in arbitrary dimensions
• Antisymmetric Wilson loops in $\mathcal{N}=4$ SYM beyond the planar limit
• Fermionic impurities in the unquenched ABJM
• Non-Local Deformation of a Supersymmetric Field Theory
• Wilson loops in $\mathcal{N}=4$ $SO(N)$ SYM and D-Branes in $Ad{S}_5\times {\mathbb{RP}}^5$
• Holographic RG Flows for Kondo-like Impurities
• Introduction to Gauge/Gravity Duality (TASI Lectures 2017)
• Gluonic fields of a static particle to all orders in 1/N
• Holographic quantum singularity
• Holographic mean field theory and Kondo lattice
• A Holographic Two-Impurity Kondo Model
• Seeing bulk perturbations in Lifshitz holography
• Near Horizon Geometry of Strings Ending on Intersecting D8/D4-branes