Dynamical heterogeneities -- strong fluctuations near the glass transition --are believed to be crucial to explain much of the glass transitionphenomenology. One possible hypothesis for their origin is that they emergefrom soft (Goldstone) modes associated with a broken continuous symmetry undertime reparametrizations. To test this hypothesis, we use numerical simulationdata from four glass-forming models to construct coarse grained observablesthat probe the dynamical heterogeneity, and decompose the fluctuations of theseobservables into two transverse components associated with the postulatedtime-fluctuation soft modes and a longitudinal component unrelated to them. Wefind that as temperature is lowered and timescales are increased, the timereparametrization fluctuations become increasingly dominant, and that theircorrelation volumes grow together with the correlation volumes of the dynamicalheterogeneities, while the correlation volumes for longitudinal fluctuationsremain small.
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