  We propose a model of the Kondo effect based on the Anti-de Sitter/Conformal
Field Theory (AdS/CFT) correspondence, also known as holography. The Kondo
effect is the screening of a magnetic impurity coupled anti-ferromagnetically
to a bath of conduction electrons at low temperatures. In a (1+1)-dimensional
CFT description, the Kondo effect is a renormalization group flow triggered by
a marginally relevant (0+1)-dimensional operator between two fixed points with
the same Kac-Moody current algebra. In the large-N limit, with spin SU(N) and
charge U(1) symmetries, the Kondo effect appears as a (0+1)-dimensional
second-order mean-field transition in which the U(1) charge symmetry is
spontaneously broken. Our holographic model, which combines the CFT and large-N
descriptions, is a Chern-Simons gauge field in (2+1)-dimensional AdS space,
AdS3, dual to the Kac-Moody current, coupled to a holographic superconductor
along an AdS2 subspace. Our model exhibits several characteristic features of
the Kondo effect, including a dynamically generated scale, a resistivity with
power-law behavior in temperature at low temperatures, and a spectral flow
producing a phase shift. Our holographic Kondo model may be useful for studying
many open problems involving impurities, including for example the Kondo
lattice problem.
