  We study Kondo physics in the algebraic spin liquid, recently proposed to
describe $ZnCu_{3}(OH)_{6}Cl_{2}$ [Phys. Rev. Lett. {\bf 98}, 117205 (2007)].
Although spin dynamics of the algebraic spin liquid is described by massless
Dirac fermions, this problem differs from the Pseudogap Kondo model, because
the bulk physics in the algebraic spin liquid is governed by an interacting
fixed point where well-defined quasiparticle excitations are not allowed.
Considering an effective bulk model characterized by an anomalous critical
exponent, we derive an effective impurity action in the slave-boson context.
Performing the large-$N_{\sigma}$ analysis with a spin index $N_{\sigma}$, we
find an impurity quantum phase transition from a decoupled local-moment state
to a Kondo-screened phase. We evaluate the impurity spin susceptibility and
specific heat coefficient at zero temperature, and find that such responses
follow power-law dependencies due to the anomalous exponent of the algebraic
spin liquid. Our main finding is that the Wilson's ratio for the magnetic
impurity depends strongly on the critical exponent in the zero temperature
limit. We propose that the Wilson's ratio for the magnetic impurity may be one
possible probe to reveal criticality of the bulk system.
