Microscopics of de Sitter Entropy from Precision Holography

We calculate quantum corrections to the entropy of four-dimensional de Sitter space induced by higherderivative terms in the gravitational action and by one-loop effects. Employing the intertwinement in semiclassical gravity of Euclidean de Sitter and anti-de Sitter saddles, we embed effective de Sitter gravity theories in M theory and express the entropy in terms of the regularized Euclidean anti-de Sitter action on an auxiliary EAdS4 x S7/7Lk background.We conjecture that the partition function of the holographically dual 3D Aharony-Bergman-Jafferis-Maldacena CFT determines the explicit form of the corrections to the de Sitter entropy. This includes a logarithmic term, the coefficient of which, we show, agrees with an independent one-loop calculation around the -S4 x S7/7Lk Euclidean de Sitter saddle. This provides evidence that the microscopic degrees of freedom behind the entropy of four-dimensional de Sitter space in gravitational theories with a holographic dual description are encapsulated by the path integral of the Euclidean CFT on the three-sphere.