We report on five compact, extremely young (< 10 Myr) and blue (beta(UV) <-2.5, F-lambda =lambda(beta)) objects observed with VLT/Multi Unit Spectroscopic Explorer at redshifts 3.1169 and 3.235, in addition to three objects at z = 6.145. These sources are strongly magnified (3-40 times) by the Hubble Frontier Field galaxy clusters MACS J0416 and AS1063. Their delensed halflight radii (R-e) are between 16 and 140 pc, the stellar masses are similar or equal to 1-20 x 10(6)M(circle dot), the magnitudes are m(UV) = 28.8-31.4 (-17 < M-UV < -15) and specific star formation rates can be as large as similar to 800 Gyr(-1). Remarkably, the inferred physical properties of two objects are similar to those expected in some globular cluster formation scenarios, representing the best candidate proto-GCs discovered so far. Rest-frame optical high-dispersion spectroscopy of one of them at z = 3.1169 yields a velocity dispersion sigma(v) similar or equal to 20 km s(-1), implying a dynamical mass dominated by the stellar mass. Another object at z = 6.145, with delensed MUV similar or equal to -15.3 (mUV similar or equal to 31.4), shows a stellarmass 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 delensed m(UV) similar or equal to 32, a stellarmass of 0.5x106M(circle dot) and a star formation rate of 0.06M(circle dot) yr(-1) 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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