Globular clusters contain multiple stellar populations with peculiar chemical compositions. Pollution of the intracluster gas by an early population of fast-evolving stars is the most common scenario for explaining the observations. Stars with masses in excess of 1000 Msun have recently been suggested as potential polluters. We investigate the spectral properties of proto-GCs that would host a supermassive star. Our main goal is to quantify how such a star would affect the integrated light of the cluster, and to study the detectability of such objects. We computed non-LTE atmosphere models for SMS with various combinations of stellar parameters (luminosity, effective temperature, and mass) and metallicities appropriate for GCs, and we predict their emergent spectra. Using these spectra, we calculated the total emission of young proto-GCs with SMS as predicted in a previously reported scenario, and we computed synthetic photometry in UV, optical, and near-IR bands, in particular for the JWST. At an effective temperature of 10000 K, the spectrum of SMSs shows a Balmer break in emission. This feature is due to strong non-LTE effects (implied by the high luminosity) and is not observed in normal stars. The hydrogen lines also show a peculiar behavior, with Balmer lines in emission while higher series lines are in absorption. At 7000 K, the Balmer break shows a strong absorption. At high effective temperatures, the Lyman break is found in emission. Cool and luminous SMSs are found to dominate the integrated spectrum of the cluster, except for the UV range. The predicted magnitudes of these proto-GCs are m_AB~28-30 between 0.7 and 8 um and for redshifts z~4-10, which is detectable with the JWST. The peculiar observational features of cool SMSs imply that they might in principle be detected in color-color diagrams that probe the spectral energy distribution below and above the Balmer break.
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