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We study the impact of Ly$\alpha$ radiation feedback on globular cluster (GC)formation. In this Letter, we analytically derive the relation between starformation efficiency (SFE) and metallicity in spherical clouds with theLy$\alpha$ radiation feedback. Our models show that the SFE becomes small asthe metallicity decreases. In metal-poor gas clouds, Ly$\alpha$ photons aretrapped for a long time and exert strong radiation force to the gas, resultingin the suppression of star formation. We find that bound star-clusters (SFE$\gtrsim$ 0.5) form only for the metallicity higher than $\sim10^{-2.5}~Z_{\odot}$ in the case with the initial cloud mass $10^5~{\rmM}_\odot$ and the radius 5 pc. Our models successfully reproduce the lowerbound of observed metallicity of GCs. Thus, we suggest that the Ly$\alpha$radiation feedback can be essential in understanding the formation of GCs.

Suppression of globular cluster formation in metal-poor gas clouds by Lyman-alpha radiation feedback