Cancellation of divergences in ${\cal N}=4$ SYM/Type IIB Supergravity correspondence
Using Schrödinger 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.
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