Weyl cohomology and the effective action for conformal anomalies - art. no. 104022

We present a general method of deriving the effective action for conformal anomalies in any even dimension, which satisfies the Wess-Zumino consistenc y condition by construction. The method relies on defining the coboundary o perator of the local Weyl group, g(ab)-->exp(2 sigma )g(ab), and giving a c ohomological interpretation to counterterms in the effective action in dime nsional regularization with respect to this group. Nontrivial cocycles of t he Weyl group arise from local functionals that are Weyl invariant in and o nly in the physical even integer dimension d = 2k. In the physical dimensio n the nontrivial cocycles generate covariant nonlocal action functionals ch aracterized by sensitivity to global Weyl rescalings. The nonlocal action s o obtained is unique up to the addition of trivial cocycles and Weyl invari ant terms, both of which are insensitive to global Weyl rescalings. These d istinct behaviors under rigid dilations can be used to distinguish between infrared relevant and irrelevant operators in a generally covariant manner. Variation of the d = 4 nonlocal effective action yields two new conserved geometric stress tensors with local traces equal to the square of the Weyl tensor and the Gauss-Bonnet-Euler density, respectively. The second of thes e conserved tensors becomes H-(3)(ab) in conformally flat spaces, exposing the previously unsuspected origin of this tensor. The method may be extende d to any even dimension by making use of the general construction of confor mal invariants given by Fefferman and Graham. As a corollary, conformal fie ld theory (CFT) behavior of correlators at the asymptotic infinity of eithe r anti-de Sitter or de. Sitter spacetimes follows, i.e., AdS(d+1)- or deS(d +1)-CFTd correspondence. The same construction naturally selects all infrar ed relevant terms (and only those terms) in the low energy effective action of gravity in any even integer dimension. The infrared relevant terms aris ing from the known anomalies in d=4 imply that the classical Einstein theor y is modified at large distances.