ALMA Observations of Massive Clouds in the Central Molecular Zone: Jeans
  Fragmentation and Cluster Formation
  We report ALMA Band 6 continuum observations of 2000 AU resolution toward
four massive molecular clouds in the Central Molecular Zone of the Galaxy. To
study gas fragmentation, we use the dendrogram method to identify cores as
traced by the dust continuum emission. The four clouds exhibit different
fragmentation states at the observed resolution despite having similar masses
at the cloud scale ($\sim$1--5 pc). Assuming a constant dust temperature of 20
K, we construct core mass functions of the clouds and find a slightly top-heavy
shape as compared to the canonical initial mass function, but we note several
significant uncertainties that may affect this result. The characteristic
spatial separation between the cores as identified by the minimum spanning tree
method, $\sim$$10^4$ AU, and the characteristic core mass, 1--7 $M_\odot$, are
consistent with predictions of thermal Jeans fragmentation. The three clouds
showing fragmentation may be forming OB associations (stellar mass $\sim$$10^3$
$M_\odot$). None of the four clouds under investigation seem to be currently
able to form massive star clusters like the Arches and the Quintuplet
($\sim$$10^4$ $M_\odot$), but they may form such clusters by further gas
accretion onto the cores.
