  We report a significant detection of the hot intergalactic medium in the
filamentary bridge connecting the galaxy clusters Abell 399 and Abell 401. This
result is enabled by a low-noise, high-resolution map of the thermal
Sunyaev-Zeldovich signal from the Atacama Cosmology Telescope (ACT) and Planck
satellite. The ACT data provide the $1.65'$ resolution that allows us to
clearly separate the profiles of the clusters, whose centres are separated by
$37'$, from the gas associated with the filament. A model that fits for only
the two clusters is ruled out compared to one that includes a bridge component
at $>5\sigma$. Using a gas temperature determined from Suzaku X-ray data, we
infer a total mass of $(3.3\pm0.7)\times10^{14}\,\mathrm{M}_{\odot}$ associated
with the filament, comprising about $8\%$ of the entire Abell 399-Abell 401
system. We fit two phenomenological models to the filamentary structure; the
favoured model has a width transverse to the axis joining the clusters of
${\sim}1.9\,\mathrm{Mpc}$. When combined with the Suzaku data, we find a gas
density of $(0.88\pm0.24)\times10^{-4}\,\mathrm{cm}^{-3}$, considerably lower
than previously reported. We show that this can be fully explained by a
geometry in which the axis joining Abell 399 and Abell 401 has a large
component along the line of sight, such that the distance between the clusters
is significantly greater than the $3.2\,\mathrm{Mpc}$ projected separation on
the plane of the sky. Finally, we present initial results from higher
resolution ($12.7"$ effective) imaging of the bridge with the MUSTANG-2
receiver on the Green Bank Telescope.
