  We investigate the shear viscosity of leptons in a strongly coupled quark
gluon plasma (QGP). We find that the shear viscosity due to the lepton-quark
scattering is inversely proportional to the ratio of electric conductivity of
the QGP to temperature up to the leading logarithmic order of the
electromagnetic coupling. The finding implies that the thermal leptons form a
more viscous fluid than the quarks by a large ratio. Using the known result for
the electrical conductivity of strongly coupled plasmas obtained from
gauge/gravity duality, we find that the lepton shear viscosity is suppressed
compared with the one from lepton-lepton scattering. Consistently, we find an
enhancement of the energy loss of hard leptons in a strongly coupled scenario
compared with that in a weakly coupled plasma.
