On nonlinear susceptibility in supercooled liquids

In this paper, we discuss theoretically the behavior of the four point nonlinear susceptibility and its associated correlation length for supercooled liquids close to the Mode Coupling instability temperature $T_c$. 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.