  Massive stars ($M > 8$ \msun) typically form in parsec-scale molecular clumps
that collapse and fragment, leading to the birth of a cluster of stellar
objects. We investigate the role of magnetic fields in this process through
dust polarization at 870 $\mu$m obtained with the Submillimeter Array (SMA).
The SMA observations reveal polarization at scales of $\lsim$ 0.1 pc. The
polarization pattern in these objects ranges from ordered hour-glass
configurations to more chaotic distributions. By comparing the SMA data with
the single dish data at parsec scales, we found that magnetic fields at dense
core scales are either aligned within $40^\circ$ of or perpendicular to the
parsec-scale magnetic fields. This finding indicates that magnetic fields play
an important role during the collapse and fragmentation of massive molecular
clumps and the formation of dense cores. We further compare magnetic fields in
dense cores with the major axis of molecular outflows. Despite a limited number
of outflows, we found that the outflow axis appears to be randomly oriented
with respect to the magnetic field in the core. This result suggests that at
the scale of accretion disks ($\lsim 10^3$ AU), angular momentum and dynamic
interactions possibly due to close binary or multiple systems dominate over
magnetic fields. With this unprecedentedly large sample massive clumps, we
argue on a statistical basis that magnetic fields play an important role during
the formation of dense cores at spatial scale of 0.01 - 0.1 pc in the context
of massive star and cluster star formation.
