  We derive a mode-coupling theory (MCT) to describe the dynamics of tracer
particles in dense systems of active Brownian particles (ABPs) in two spatial
dimensions. The ABP undergo translational and rotational Brownian dynamics, and
are equipped with a fixed self-propulsion speed along their orientational
vector that describes their active motility. The resulting equations of motion
for the tagged-particle density correlation functions describe the various
cases of tracer dynamics close to the glass transition: that of a passive
colloidal particle in a suspension of ABP, that of a single active particle in
a glass-forming passive host suspensions, and that of active tracers in a bath
of active particles. Numerical results are presented for these cases assuming
hard-sphere interactions among the particles. The qualitative and quantitative
accuracy of the theory is tested against event-driven Brownian dynamics (ED-BD)
simulations of active and passive hard disks. Simulation and theory are found
in quantitative agreement, provided one adjusts the overall density (as known
from the passive description of glassy dynamics), and allows for a rescaling of
self-propulsion velocities in the active host system. These adjustments account
for the fact that ABP-MCT generally overestimates the tendency for kinetic
arrest. We also confirm in the simulations a peculiar feature of the transient
and stationary dynamical density correlation functions regarding their lack of
symmetry under time reversal, demonstrating the non-equilibrium nature of the
system and how it manifests itself in the theory.
