  A bottom-up Einstein-Maxwell-Dilaton holographic model is used to compute,
for the first time, the behavior of several transport coefficients of the hot
and baryon-rich strongly coupled quark-gluon plasma at the critical point and
also across the first-order phase transition line in the phase diagram. The
observables under study are of the shear and bulk viscosities, baryon
diffusion, thermal conductivity, the jet quenching parameter $\hat{q}$, as well
as the heavy-quark drag force and Langevin diffusion coefficients. These
calculations provide a phenomenologically promising estimate for these
coefficients, given that our model quantitatively reproduces lattice QCD
thermodynamics results, both at zero and finite baryon density, besides
naturally incorporating the nearly-perfect fluidity of the quark-gluon plasma.
We find that the diffusion of baryon charge, and also the shear and bulk
viscosities, are suppressed with increasing baryon density, indicating that the
medium becomes even closer to perfect fluidity at large densities. On the other
hand, the jet quenching parameter and the heavy-quark momentum diffusion are
enhanced with increasing density. The observables display a discontinuity gap
when crossing the first-order phase transition line, while developing an
infinite slope at the critical point. The transition temperatures associated
with different transport coefficients differ in the crossover region but are
found to converge at the critical point.
