The Boundary Weyl Anomaly in the ${\cal N}=4$ SYM/Type IIB Supergravity Correspondence

TL;DR

This paper computes the Weyl anomaly of ${ m N}=4$ SYM using the AdS/CFT correspondence, including $1/N^2$ corrections from Type IIB Supergravity fields, providing a stringent test of the duality.

Contribution

It offers a complete Schr"odinger representation approach to match the Weyl anomaly including all supergravity fields' contributions.

Findings

Successful matching of the $1/N^2$ correction with CFT results

Universal formula for each supergravity field's contribution

Non-trivial test confirming the AdS/CFT correspondence

Abstract

We give a complete account of the Schr\"odinger representation approach to the calculation of the Weyl anomaly of ${\cal N}=4$ SYM from the AdS/CFT correspondence. On the AdS side, the $1/N^2$ correction to the leading order result receives contributions from all the fields of Type IIB Supergravity, the contribution of each field being given by a universal formula. The correct matching with the CFT result is thus a highly non-trivial test of the correspondence.