  Suppression of open heavy flavors and quarkonia in heavy-ion collisions is
among the most informative probes of the quark-gluon plasma. Interpreting the
full wealth of data obtained from the collision events requires a precise
understanding of the evolution of heavy quarks and quarkonia as they propagate
through the nearly thermal and strongly coupled plasma. Systematic theoretical
studies of quarkonium time evolution in the QGP in the regime where the
temperature of the QGP is much smaller than the inverse of quarkonium size have
only been carried out in the past few years. Such calculations require the
evaluation of a gauge-invariant correlator of chromoelectric fields dressed
with Wilson lines, which is similar to, but different from, the correlation
used to define the well-known arXiv:hep-ph/0605199 heavy quark diffusion
coefficient. The origin of this difference has been explained in
arXiv:2107.03945, arXiv:2205.04477, arXiv:2306.13127. Here we show the results
of the calculation of the analogous correlator in strongly coupled
$\mathcal{N}=4$ SYM using the AdS/CFT correspondence at a finite temperature
arXiv:2304.03298. While it resembles the open heavy quark case, it has some
crucial differences that highlight the relevance of quantum color correlations.
We will also discuss the results for the quarkonium transport coefficients
obtained from this correlator, thereby establishing the first analytic results
at strong coupling in this context. We find that they vanish in the strong
coupling limit for an $\mathcal{N}=4$ SYM plasma with a large number of colors.
