GMRT 610 MHz observations of galaxy clusters in the ACT equatorial
  sample
  We present Giant Metrewave Radio Telescope 610 MHz observations of 14 Atacama
Cosmology Telescope (ACT) clusters, including new data for nine. The sample
includes 73\% of ACT equatorial clusters with $M_{500} > 5 \times
10^{14}\;M_\odot$. We detect diffuse emission in three of these
(27$^{+20}_{-14}$\%): we detect a radio mini-halo in ACT-CL J0022.2$-$0036 at
$z=0.8$, making it the highest-redshift mini-halo known; we detect potential
radio relic emission in ACT-CL J0014.9$-$0057 ($z=0.533$); and we confirm the
presence of a radio halo in low-mass cluster ACT-CL J0256.5+0006, with flux
density $S_{610} = 6.3\;\pm\;0.4$ mJy. We also detect residual diffuse emission
in ACT-CL J0045.9$-$0152 ($z=0.545$), which we cannot conclusively classify.
For systems lacking diffuse radio emission, we determine radio halo upper
limits in two ways and find via survival analysis that these limits do not
significantly affect radio power scaling relations. Several clusters with no
diffuse emission detection are known or suspected mergers, based on archival
X-ray and/or optical measures; given the limited sensitivity of our
observations, deeper observations of these disturbed systems are required in
order to rule out the presence of diffuse emission consistent with known
scaling relations. In parallel with our diffuse emission results, we present
catalogs of individual radio sources, including a few interesting extended
sources. Our study represents the first step towards probing the occurrence of
diffuse emission in high-redshift ($z\gtrsim0.5$) clusters, and serves as a
pilot for statistical studies of larger cluster samples with the new radio
telescopes available in the pre-SKA era.
