Summary: We follow Witten’s proposal 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 \(L= aR^2+ bR_{\mu\nu} R^{\mu\nu}+ \Lambda\) (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 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).

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