On the Conformal Anomaly from Higher Derivative Gravity in AdS/CFT Correspondence

We follow Witten's proposal¹ 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 description in terms of above (d+1)-dimensional higher derivative gravity which includes not only the Einstein term and cosmological constant but also curvature 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=aR²+bR_μνR^μν+Λ (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 gives new versions of bulk side which may be useful in different aspects. As application 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).