  Glass-forming liquids grow dramatically sluggish upon cooling. This slowdown
has long been thought to be accompanied by a growing correlation length.
Characteristic dynamical and static length scales, however, have been observed
to grow at different rates, which perplexes the relationship between the two
and with the slowdown. Here, we show the existence of a direct link between
dynamical sluggishness and static point-to-set correlations, holding at the
local level as we probe different environments within a liquid. This link,
which is stronger and more general than that observed with locally preferred
structures, suggests the existence of an intimate relationship between
structure and dynamics in a broader range of glass-forming liquids than
previously thought.
