  Most molecular clouds are filamentary or elongated. Among those forming
low-mass stars, their long axes tend to be either parallel or perpendicular to
the large-scale (10-100 pc) magnetic field (B-field) in the surrounding inter
cloud medium. This arises because, along the dynamically dominant B-fields, the
competition between self-gravity and turbulent pressure will shape the cloud to
be elongated either perpendicular or parallel to the fields. Recent study also
suggested that, on the scales of 0.1-0.01 pc, fields are dynamically important
within cloud cores forming massive stars. But whether the core field
morphologies are inherited from the inter cloud medium or governed by cloud
turbulence is under vigorous debate, so is the role played by B-fields in cloud
fragmentation at 10 - 0.1 pc scales. Here we report B-field maps covering
100-0.01 pc scales inferred from polarimetric observations of a massive-star
forming region, NGC 6334. First, the main filament also lies perpendicular to
the ambient field. NGC 6334 hosts young star-forming sites where fields are not
severely affected by stellar feedback, and their directions do not change
significantly over the entire scale range. This means that the fields are
dynamically important. At various scales, we find that the hourglass-shaped
field lines are pinched where the gas column density peaks and the field
strength is proportional to the 0.4-power of the density. We conclude that
B-fields play a crucial role in the fragmentation of NGC 6334.
