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

TL;DR

This paper provides a nonperturbative holographic calculation of the boundary Weyl anomaly for ${ m N}=4$ SYM by summing one-loop contributions from all fields in Type IIB supergravity on ${ m AdS}_5 imes S^5$. By recasting the bulk theory in a Schrödinger-wave framework with boundary sources, the authors derive a universal relation ${ m abla A} = -( riangle-2)rac{a_2}{32\\pi^2}$ for each five-dimensional field, and then sum over the full Kaluza–Klein spectrum to reproduce the subleading anomaly term ${ m A}$ of the SYM theory, confirming the Maldacena conjecture at this order. They carefully diagonalise the spectrum for gravitons, antisymmetric tensors, vectors, and fermions, accounting for mass terms, gauge-fixing ghosts, and zero modes, and demonstrate that the total anomaly is governed by a simple combination of four-dimensional heat-kernel coefficients, matching the known field-theory result. The methodology is robust and extendable to other AdS/CFT correspondences, highlighting a universal mechanism by which bulk quantum effects encode boundary conformal data. The work thereby strengthens the case for holography by connecting bulk one-loop dynamics to precise boundary anomaly coefficients through a coherent, operator-based framework.

Abstract

We give a complete account of the Schrödinger 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.