Order $1/N^2$ test of the Maldacena conjecture II: the full bulk one-loop contribution to the boundary Weyl anomaly

TL;DR

This paper calculates the full one-loop bulk contribution to the boundary Weyl anomaly in IIB Supergravity on AdS5×S5, confirming the Maldacena conjecture at subleading order in N and highlighting the complexity of boundary theory beyond leading order.

Contribution

It provides the complete bulk one-loop correction to the Weyl anomaly, demonstrating the subleading term matches the boundary theory prediction and questioning the truncation to massless multiplets.

Findings

Reproduces the subleading term in the Weyl anomaly of N=4 Super-Yang-Mills.

Confirms the Maldacena conjecture at one-loop order.

Shows contributions from all multiplets, challenging simplified truncation models.

Abstract

We compute the complete bulk one-loop contribution to the Weyl anomaly of the boundary theory for IIB Supergravity compactified on $ AdS_5\times S^5$. The result, that $\delta {\cal A}=(E+I)/(2\pi^2)$, reproduces the subleading term in the exact expression ${\cal A}=-(N^2-1)(E+I)/(2\pi^2)$ for the Weyl anomaly of ${\cal N}=4$ Super-Yang-Mills theory, confirming the Maldacena conjecture. The anomaly receives contributions from all multiplets casting doubt on the possibility of describing the boundary theory beyond leading order in $N$ by a consistent truncation to the `massless' multiplet of IIB Supergravity.