  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.
