  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 $-i \langle {\cal O} \rangle^2$, which
is characteristic of a Kondo resonance.
