Some cubic couplings in type IIB supergravity onAdS5×S5and three-point functions in four-dimensional super Yang-Mills theory at largeN

All cubic couplings in type IIB supergravity on ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ that involve two scalar fields $s^I$ that are mixtures of the five form field strength on ${\mathrm{S}}^5$ and the trace of the graviton on ${\mathrm{S}}^5$ are derived by using the covariant equations of motion and the quadratic action for type IIB supergravity on ${\mathrm{AdS}}_5\times {\mathrm{S}}^5.$ All corresponding three-point functions in ${\mathrm{SYM}}_4$ are calculated in the supergravity approximation. It is pointed out that the scalars $s^I$ correspond not to the chiral primary operators in the $\mathcal{N}=4\mathrm{}$ SYM but rather to a proper extension of the operators.