Using Schr\"odinger functional methods, we show that in the ${ \cal N}=4$ SYM/Type IIB Supergravity correspondence the renormalisation of the boundary Newton and gravitational constants arising from bulk fields cancels when we sum over all the Kaluza-Klein modes of Supergravity. This accords with the expected finiteness of ${ \cal N}=4$ SYM, and it is expected that other renormalisations cancel in a similar way.
Categories: hep-th