TACHYONS IN DE SITTER SPACE AND ANALYTICAL CONTINUATION FROM dS/CFT TO AdS/CFT

We discuss analytic continuation from d-dimensional Lorentzian de Sitter (dSd) to d-dimensional Lorentzian anti-de Sitter (AdSd) space–time. We show that AdSd, with opposite signature of the metric, can be obtained as analytic continuation of a portion of dSd. This implies that the dynamics of (positive square-mass) scalar particles in AdSd can be obtained from the dynamics of tachyons in dSd. 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.