  Thermal tides can torque the atmosphere of hot Jupiters into asynchronous
rotation, while these planets are usually assumed to be locked into spin-orbit
synchronization with their host star. In this work, our goal is to characterize
the tidal response of a rotating hot Jupiter to the tidal semidiurnal thermal
forcing of its host star, by identifying the structure of tidal waves
responsible for variation of mass distribution, their dependence on the tidal
frequency and their ability to generate strong zonal flows. We develop an ab
initio global modeling that generalizes the early approach of Arras & Socrates
(2010) to rotating and non-adiabatic planets. We derive analytically the torque
exerted on the body and the associated timescales of evolution, as well as the
equilibrium tidal response of the atmosphere in the zero-frequency limit.
Finally, we integrate numerically the equations of thermal tides for three
cases including dissipation and rotation step by step. The resonances
associated with tidally generated gravito-inertial waves amplify significantly
the resulting tidal torque in the range 1-30 days. This torque can drive
globally the atmosphere into asynchronous rotation, as its sign depends on the
tidal frequency. The resonant behaviour of the tidal response is enhanced by
rotation, which couples the forcing to several Hough modes in the general case,
while the radiative cooling tends to regularize it and diminish its amplitude.
