  We discuss analytic continuation from d-dimensional Lorentzian de Sitter
(dS$_d$) to d-dimensional Lorentzian anti-de Sitter (AdS$_{d}$) spacetime. We
show that AdS$_{d}$, with opposite signature of the metric, can be obtained as
analytic continuation of a portion of dS$_d$. This implies that the dynamics of
(positive square-mass) scalar particles in AdS$_{d}$ can be obtained from the
dynamics of tachyons in dS$_d$. We discuss this correspondence both at the
level of the solution of the field equations and of the Green functions. The
AdS/CFT duality is obtained as analytic continuation of the dS/CFT duality.
