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At the microscopic level, equilibrium liquid's translational symmetry is spontaneously broken at the so-called dynamic glass transition predicted by the mean-field replica approach. We show that this fact implies the emergence of Goldstone modes and long-range density correlations. We derive and evaluate a new statistical mechanical expression for the glass shear modulus.doi:10.1103/physrevlett.107.105505 pmid:21981512 fatcat:5ihpaerijradtnfkbbbxpcgmdy