  By analyzing two Kinetically Constrained Models of supercooled liquids we
show that the anomalous transport of a driven tracer observed in supercooled
liquids is another facet of the phenomenon of dynamical heterogeneity. We focus
on the Fredrickson-Andersen and the Bertin-Bouchaud-Lequeux models. By
numerical simulations and analytical arguments we demonstrate that the
violation of the Stokes-Einstein relation and the observed field-induced
superdiffusion have the same physical origin: while a fraction of probes do not
move, others jump repeatedly because they are close to local mobile regions.
The anomalous fluctuations observed out of equilibrium in presence of a pulling
force $\epsilon$, $\sigma_x^2(t) = \langle x_\epsilon^2(t) \rangle - \langle
x_\epsilon(t) \rangle^2 \sim t^{3/2}$, which are accompanied by the asymptotic
decay $\alpha_\epsilon(t)\sim t^{-1/2}$ of the non-Gaussian parameter from
non-trivial values to zero, are due to the splitting of the probes population
in the two (mobile and immobile) groups and to dynamical correlations, a
mechanism expected to happen generically in supercooled liquids.
