  We present a mode-coupling theory (MCT) for the high-density dynamics of
two-dimensional spherical active Brownian particles (ABP). The theory is based
on the integration-through-transients (ITT) formalism and hence provides a
starting point for the calculation of non-equilibrium averages in
active-Brownian particle systems. The ABP are characterized by a
self-propulsion velocity $v_0$, and by their translational and rotational
diffusion coefficients, $D_t$ and $D_r$. The theory treats both the
translational and the orientational degrees of freedom of ABP explicitly. This
allows to study the effect of self-propulsion of both weak and strong
persistence of the swimming direction, also at high densities where the
persistence length $\ell_p=v_0/D_r$ is large compared to the typical
interaction length scale. While the low-density dynamics of ABP is
characterized by a single P\'eclet number, $Pe=v_0^2/D_rD_t$, close to the
glass transition the dynamics is found to depend on $Pe$ and $\ell_p$
separately. At fixed density, increasing the self-propulsion velocity causes
structural relaxatino to speed up, while decreasing the persistence length
slows down the relaxation. The theory predicts a non-trivial
idealized-glass-transition diagram in the three-dimensional parameter space of
density, self-propulsion velocity and rotational diffusivity. The active-MCT
glass is a nonergodic state where correlations of initial density fluctuations
never fully decay, but also an infinite memory of initial orientational
fluctuations is retained in the positions.
