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.
Categories: hep-th