Cubic couplings in D Ä 6 , N Ä 4 b supergravity on AdS 3 Ã S

The AdS–conformal field theory correspondence provides information about the strong coupling behavior of some conformal field theories by studying their supergravity ~string! duals @1–4#. In particular, the AdS-CFT duality relates type IIB string theory on AdS33S 3M, where M is either K3 or T, to a certain N5(4,4) supersymmetric twodimensional conformal field theory ~CFT! living on the boundary of AdS3. A two-dimensional sigma model with the target space being a deformation of the orbifold symmetric product S(M )5(M )/SN , N→` , is believed to provide an effective description of this CFT @5#. An important class of operators in the supersymmetric CFT are the chiral primary operators ~CPOs! since they are annihilated by 1/2 of the supercharges and in two dimensions their highest weight components of the R-symmetry group form a ring. On the gravity side the CPOs correspond to Kaluza-Klein ~KK! modes of the type IIB supergravity compactification. Recently, using the orbifold technique developed in @6# the three-point functions of scalar CPOs were computed @7# in the CFT on the symmetric product S(M ) and, on the other hand, in AdS33S 3 supergravity @8#, and were found to disagree. On the other hand, computations of quantities that are stable under deformations of the orbifold CFT, like the spectrum of the CPOs and the elliptic genus, were found to be in complete agreement @10#. Obviously this supports the expectation that the AdS33S 3 background may correspond to some deformation of the target space S(M ) of the boundary CFT. However, even though one presently does not have an explicit sigma model formulation of the boundary CFT ~see also @11# for recent developments!, one may proceed to study the CFT by using directly the gravity dual description and the AdS-CFT correspondence @12#.