  Massive companions in close orbits around G dwarfs are thought to undergo
rapid orbital decay due to runaway tidal dissipation. We report here the
discovery of WASP-128b, a brown dwarf discovered by the WASP survey transiting
a G0V host on a $2.2\,\mathrm{d}$ orbit, where the measured stellar rotation
rate places the companion in a regime where tidal interaction is dominated by
dynamical tides. Under the assumption of dynamical equilibrium, we derive a
value of the stellar tidal quality factor $\log{Q_\star'} = 6.96 \pm 0.19$. A
combined analysis of ground-based photometry and high-resolution spectroscopy
reveals a mass and radius of the host, $M_\star = 1.16 \pm 0.04\,M_\odot$,
$R_\star = 1.16 \pm 0.02\,R_\odot$, and for the companion, $M_\mathrm{b} =37.5
\pm 0.8\,M_\mathrm{Jup}$, $R_\mathrm{b} = 0.94 \pm 0.02\,R_\mathrm{Jup}$,
placing WASP-128b in the driest parts of the brown dwarf desert, and suggesting
a mild inflation for its age. We estimate a remaining lifetime for WASP-128b
similar to that of some ultra-short period massive hot Jupiters, and note it
may be a propitious candidate for measuring orbital decay and testing tidal
theories.
