  We derive the quadratic action of the fluctuations around the classical world
sheet underlying the jet quenching from AdS/CFT. After obtaining the
correspondence partition function, the expansion of the jet quenching parameter
of $\mathcal N=4$ super symmetric Yang-Mills theory is carried out to the
sub-leading term in the large 't Hooft coupling $\lambda$ at a nonzero
temperature. The strong coupling corresponds to the semi-classical expansion of
the string-sigma model, the gravity dual of the Wilson loop operator, with the
sub-leading term expressed in terms of functional determinants of fluctuations.
The contribution of these determinants are evaluated numerically. We find the
jet quenching parameter is reduced due to world sheet fluctuations by a factor
$(1-1.97\lambda^{-1/2}) $
