  Recent Atacama Large Millimeter/submillimeter Array (ALMA) observations of
protoplanetary disks in the millimeter continuum have shown a variety of radial
gaps, cavities, and spiral features. These substructures may be signposts for
ongoing planet formation, and therefore these systems are promising targets for
direct imaging planet searches in the near-infrared. To this end, we present
results from a deep imaging survey in the $L'$-band (3.8 $\mu$m) with the
Keck/NIRC2 vortex coronagraph to search for young planets in 43 disks with
resolved features in the millimeter continuum or evidence for gaps/central
cavities from their spectral energy distributions. Although we do not detect
any new point sources, using the vortex coronagraph allows for high sensitivity
to faint sources at small angular separations (down to
${\sim}$0$^{\prime\prime}$.1), allowing us to place strong upper limits on the
masses of potential gas giant planets. We compare our mass sensitivities to the
masses of planets derived using ALMA observations, and while we are sensitive
to $\sim$1 M$_{Jup}$ planets in the gaps in some of our systems, we are
generally not sensitive to planets of the masses expected from the ALMA
observations. In addition to placing upper limits on the masses of gas giant
planets that could be interacting with the dust in the disks to form the
observed millimeter substructures, we are also able to map the micron-sized
dust as seen in scattered light for 8 of these systems. Our large sample of
systems also allows us to investigate limits on planetary accretion rates and
disk viscosities.
