On the conformal anomaly from higher derivative gravity in AdS/CFT correspondence

We follow Witten's proposal(1) in the calculation of conformal anomaly from (d + 1)-dimensional higher derivative gravity via AdS/CFT correspondence. It is assumed that some d-dimensional conformal field theories have a descr iption in terms of above (d + 1)-dimensional higher derivative gravity whic h includes not only the Einstein term and cosmological constant but also cu rvature squared terms. The explicit expression for two-dimensional and four -dimensional anomalies is found, it contains higher derivative corrections. In particular, it is shown that not only Einstein gravity but also theory with the Lagrangian L = aR(2) + bR(mu nu),R-mu nu + Lambda (even when a = 0 or b = 0) is five-dimensional bulk theory for d = 4 N = 4 super-Yang-Mills theory in AdS/CFT correspondence. Similarly, the d + 1 = 3 theory with (or without) Einstein term may describe d = 2 scalar or spinor CFT's. That giv es new versions of bulk side which may be useful in different aspects. As a pplication of our general formalism we find next-to-leading corrections to the conformal anomaly of N = 2 supersymmetric theory from d = 5 AdS higher derivative gravity (low energy string effective action).