  In this paper we formulate the $xp$ model on the AdS$_2$ spacetime. We find
that the spectrum of the Hamiltonian has positive and negative eigenvalues,
whose absolute values are given by a harmonic oscillator spectrum, which in
turn coincides with that of a massive Dirac fermion in AdS$_2$. We extend this
result to generic $xp$ models which are shown to be equivalent to a massive
Dirac fermion on spacetimes whose metric depend of the $xp$ Hamiltonian.
Finally, we construct the generators of the isometry group SO(2,1) of the
AdS$_2$ spacetime, and discuss the relation with conformal quantum mechanics.
