  We have studied the Kondo effect of a spin-1/2 impurity coupled to a
two-dimensional altermagnet host material. To attain the low-temperature
many-body Kondo physics of the system, we have performed a numerical
renormalization group calculations that allows us to access the spectral
properties of the system at zero temperature. The impurity spectral function
and the Kondo temperature were calculated for different set of parameters,
including Rashba spin-orbit coupling (RSOC) and an external magnetic field.
Interestingly, in the RSOC and altermagnetic fields, the hybridization function
is spin independent, despite the characteristic broken time-reversal symmetry
of the altermagnet. This is because the alternating sign of the spin splitting
of the bands in the momentum space renders equal contributions for both spin
components of the hybridization function. Our results demonstrate that,
although the hybridization function is time-reversal symmetric, the Kondo
temperature is substantially suppressed by the altermagnet coupling. Moreover,
we have investigated the effect of an external magnetic field applied in the
altermagnet along different directions. Interestingly, we observe an important
restraining of the Kondo peak which depends strongly on the direction of the
field. This anisotropic effect is, however, masked if strong Zeeman splitting
takes place at the impurity, as it shatters the Kondo-singlet state.
