We report on five compact, extremely young (<10Myr) and blue (beta_UV<-2.5, F_lambda =lambda^beta) objects observed with VLT/MUSE at redshift 3.1169, 3.235, in addition to three objects at z=6.145. These sources are magnified by the Hubble Frontier Field galaxy clusters MACS~J0416 and AS1063. Their de-lensed half light radii (Re) are between 16 to 140pc, the stellar masses are ~1-20 X 10^6 Msun, the magnitudes are m_uv=28.8 - 31.4 (-17<Muv<-15) and specific star formation rates can be as large as ~800Gyr^-1. Multiple images of these systems are widely separated in the sky (up to 50) and individually magnified by factors 3-40. Remarkably, the inferred physical properties of two objects are similar to those expected in some globular cluster formation scenarios, representing the best candidate proto-globular clusters (proto-GC) discovered so far. Rest-frame optical high dispersion spectroscopy of one of them at z=3.1169 yields a velocity dispersion sigma_v~20km/s, implying a dynamical mass dominated by the stellar mass. Another object at z=6.145, with de-lensed Muv ~ -15.3 (m_uv ~ 31.4), shows a stellar mass and a star-formation rate surface density consistent with the values expected from popular GC formation scenarios. An additional star-forming region at z=6.145, with de-lensed m_uv ~ 32, a stellar mass of 0.5 X 10^6 Msun and a star formation rate of 0.06 Msun/yr is also identified. These objects currently represent the faintest spectroscopically confirmed star-forming systems at z>3, elusive even in the deepest blank fields. We discuss how proto-GCs might contribute to the ionization budget of the universe and augment Lya visibility during reionization. This work underlines the crucial role of JWST in characterizing the rest-frame optical and near-infrared properties of such low-luminosity high-z objects.
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