D = 4 super Yang-Mills, D = 5 gauged supergravity and D = 4 conformal supergravity Original Research Article

We consider the role of N = 4 conformal supergravity in the duality relation between N = 4 SYM theory and D = 5 gauged supergravity expanded near the anti-de Sitter background. We discuss the structure of the SYM effective action in the conformal supergravity background, in particular, terms related to conformal anomaly. Solving the leading-order Dirichlet problem for the metric perturbation in AdS background we explicitly compute the bilinear graviton term in the D = 5 Einstein action, demonstrating its equivalence to the linearised Weyl tensor squared part of the gravitational effective action induced by SYM theory. We also compute the graviton-dilaton-dilaton three-point function which is found to have the form consistent with conformal invariance of the boundary theory.