Conformal anomaly from dS / CFT correspondence

In frames of dS/CFT correspondence suggested by Strominger we calculate holographic conformal anomaly for dual euclidean CFT. The holographic renormalization group method is used for this purpose. It is explicitly demonstrated that two-dimensional and four-dimensional conformal anomalies (or corresponding central charges) have the same form as those obtained in AdS/CFT duality. [email protected] 2 [email protected], [email protected] 1 AdS/CFT duality (for a review, see [1]) relates quantum gravity on AdS D-dimensional space with boundary CFT in one dimension less. It has been proven to be very useful in modern string/quantum gravity/conformal theories. It is suspected that AdS/CFT correspondence is manifestation of some more deep fundamental principle somehow related with holography. In the recent paper by Strominger [2] it has been suggested dS/CFT correspondence in the similar sense as above AdS/CFT correspondence. The fact that quantum gravity in de Sitter space may have some holographic dual has been already mentioned in several papers [3, 4, 5, 6]. The following simple arguments may be suggested. The reason why AdS/CFT can be expected is the isometry of d + 1-dimensional anti-de Sitter space, which is SO(d, 2) symmetry. It is identical with the conformal symmetry of d-dimensional Minkowski space. We should note, however, the d+ 1-dimensional de Sitter space has the isometry of SO(d+ 1, 1) symmetry, which can be a conformal symmetry of d-dimensional Euclidean space. Then it might be natural to expect the correspondence between d + 1-dimensional de Sitter space and d-dimensional euclidean conformal symmetry (dS/CFT correspondence[2]). In fact, the metric of D = d + 1-dimensional anti de Sitter space (AdS) is given by ds2AdS = dr 2 + e (