  We investigate the relation between the star formation rate (SFR) and the
stellar mass (M), i.e. the Main Sequence (MS) relation of star-forming
galaxies, at 1.3<=z<6 in the first four HST Frontier Fields, based on
rest-frame UV observations. Gravitational lensing combined with deep HST
observations allows us to extend the analysis of the MS down to stellar masses
as low as logM/Msun~7.5 at z<~4 and logM/Msun~8 at higher redshifts, a factor
of ~10 below most previous results. We perform an accurate simulation to take
into account the effect of observational uncertainties on the MS and correct
for the Eddington bias. This step allows us to reliably measure the MS and in
particular its slope. While the normalization increases with redshift, we fit
an unevolving and approximately linear slope. We nicely extend to lower masses
the results of brighter surveys. Thanks to the large dynamic range in mass and
by making use of the simulation, we analyzed any possible mass dependence of
the dispersion around the MS. We find tentative evidence that the scatter
decreases with increasing stellar masses, suggesting a larger variety of star
formation histories in low mass galaxies. This trend agrees with theoretical
predictions, and is explained as either a consequence of the smaller number of
progenitors of low mass galaxies in a hierarchical scenario and/or of the
efficient but intermittent stellar feedback processes in low mass halos.
Finally, we observe an increase in the SFR per unit stellar mass with redshift
milder than predicted by theoretical models, implying a still incomplete
understanding of the processes responsible for galaxy growth.
