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

TL;DR

This paper demonstrates that divergences in the boundary gravitational constants cancel out in the ${ m AdS}_5/{ m CFT}_4$ correspondence for ${ m N}=4$ SYM due to the summation over all Kaluza-Klein modes, supporting the theory's finiteness.

Contribution

It shows that the renormalisation of boundary gravitational constants cancels when summing over all supergravity modes, confirming expected finiteness in the ${ m N}=4$ SYM/Type IIB supergravity duality.

Findings

Divergences in boundary Newton and gravitational constants cancel out.

Summation over all Kaluza-Klein modes leads to finiteness.

Supports the finiteness conjecture of ${ m N}=4$ SYM in holography.

Abstract

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.