  The combination of non-Hermitian physics and strong correlations can give
rise to new effects in open quantum many-body systems with balanced gain and
loss. We propose a generalized Anderson impurity model that includes
non-Hermitian hopping terms between an embedded quantum dot and two wires.
These non-Hermitian hopping terms respect a parity-time ($\mathcal{PT}$)
symmetry. In the regime of a singly occupied localized state, we map the
problem to a $\mathcal{PT}$-symmetric Kondo model and study the effects of the
interactions using a perturbative renormalization group approach. We find that
the Kondo effect persists if the couplings are below a critical value that
corresponds to an exceptional point of the non-Hermitian Kondo interaction. On
the other hand, in the regime of spontaneously broken $\mathcal{PT}$ symmetry,
the Kondo effect is suppressed and the low-energy properties are governed by a
local-moment fixed point with vanishing conductance.
