In this paper, we discuss theoretically the behaviour of the four-point non-linear susceptibility and its associated correlation length for supercooled liquids close to the mode-coupling instability temperature Tc. We work in the theoretical framework of the glass transition as described by mean-field theory of disordered systems, and the hypernetted-chain approximation. Our results give an interpretation framework for recent numerical findings on heterogeneities in supercooled liquid dynamics.
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