An xp model on AdS2 spacetime

In this paper we formulate the xp model on the AdS2 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 AdS2. 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)SO(2,1) of the AdS2 spacetime, and discuss the relation with conformal quantum mechanics.