On the origin of supergravity boundary terms in the AdS/CFT correspondence

The standard formulation of the AdS/CFT correspondence is incomplete since it requires adding to a supergravity action some a priori unknown boundary terms. We suggest a modification of the correspondence principle based on t he Hamiltonian formulation of the supergravity action, which does not requi re any boundary terms. Then all the boundary terms of the standard formulat ion naturally appear by passing from the Hamiltonian version to the Lagrang ian one. As examples the graviton part of the supergravity action on the pr oduct of AdS(d+1) with a compact Einstein manifold epsilon and fermions on AdS(d+1) are considered. We also discuss conformal transformations of gravi ty fields on the boundary of AdS and show that they are induced by the isom etries of AdS. (C) 1999 Published by Elsevier Science B.V.