  We test a hypothesis for the origin of dynamical heterogeneity in slowly
relaxing systems, namely that it emerges from soft (Goldstone) modes associated
with a broken continuous symmetry under time reparametrizations. We do this by
constructing coarse grained observables and decomposing the fluctuations of
these observables into transverse components, which are associated with the
postulated time-fluctuation soft modes, and a longitudinal component, which
represents the rest of the fluctuations. Our test is performed on data obtained
in simulations of four models of structural glasses. As the hypothesis
predicts, we find that the time reparametrization fluctuations become
increasingly dominant as temperature is lowered and timescales are increased.
More specifically, the ratio between the strengths of the transverse
fluctuations and the longitudinal fluctuations grows as a function of the
dynamical susceptibility, \chi 4, which represents the strength of the
dynamical heterogeneity; and the correlation volumes for the transverse
fluctuations are approximately proportional to those for the dynamical
heterogeneity, while the correlation volumes for the longitudinal fluctuations
remain small and approximately constant.
